text:
# [NTG-context] Spacing for {\cal P} in XITS

Janne Junnila janne.junnila at gmail.com
Tue May 29 12:19:00 CEST 2012

Hi,

I just noticed that the spacing after ${\cal P}$ looks a bit too tight
(non-existent?) while using XITS fonts.

\setupbodyfont[xits]
\starttext
The spacing of ${\cal P}$ looks like this.
\stoptext

I'm not sure if the other calligraphic letters are totally fine
either, but this one caught my eye. I suppose it's a font issue. Any
ideas?

Best regards,
Janne Junnila


text:
# Sudden Approximation Perturbation Theory

First-order ground state perturbation theory There are not many quantum problems that can be solved exactly, so approximation methods are very important. The author use perturbation theory to derive the result $$T<<\hbar/\delta \overline{H}$$,when the Hamiltonian change over time T. Substituting we get the approximation The exact solution, up to 9 decimal places, is -1. The problem of computing the best rank-(p,q,r) approximation of a third order tensor is considered. ★ This looks like second order perturbation theory but is more general since the coupling of the ,a' space functions via the perturbing operator H1 is taken into account. Unlike the infinite order sudden approximation (IOS), it converges properly at large impact parameters. Simplified algorithmic flowchart of the Perturbation Theory approximation showing the first two perturbation orders. Hence, we can use much of what we already know about linearization. Nature of the Paper. 221A Lecture Notes Time-Dependent Perturbation Theory 1 Introduction The time-independent perturbation theory is very successful when the system posses a small dimensionless parameter. Many-Body Perturbation Theory The GW approximation C. In simpler terms, a quantum mechanical system subjected to gradually changing external conditions adapts its functional form, but when subjected to rapidly varying conditions there is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged. As i read in your article this time, i didn't expect that the nature and equations of the theory will goes like that. Phase shifts. 2 Phenomenological theory of lattice dynamics Within the adiabatic approximation, the statics and dynamics of the ions are governed by an effective potential (R) = V ii(R)+E 0(R); (9) where E. For the Variational method approximation, the calculations begin with an uncorrelated wavefunction in which both electrons are placed in a hydrogenic orbital with scale factor $$\alpha$$. If the system is initially in the vibrational stationary state m this means that a m ( t ) stays close to unity and a n ( t ), n ≠ m , close to zero. Homework Statement In a beta decay H3 -> He3+, use the sudden perturbation approximation to determine the probability of that an electron initially in the 1s state of H3 will end up in the |n=16,l=3,m=0> state of He3+ Homework Equations | and |nlm> in spherical coordinates to calculate. is V^ (0) k +H^0 (1) k = E (1) k k +E 0) k k or, using the zero-order results V^ E(1) k k = ek H^0 (1) k By the completeness principle, we can always express (1) k in. Symmetry of the hydrogen atom, Lenz's vector, etc (Baym ch 7). • Time-dependent perturbation theory • Application to two level systems • The sudden and adiabatic approximations. In particular, second- and third-order approximations are easy to compute and notably improve accuracy. Rotations and Angular Momentum (Sakurai ch 3). In such cases, the time depen-dence of a wavepacket can be developed through the time-evolution operator, Uˆ = e−iHt/ˆ ! or, when cast in terms of the eigenstates of the Hamiltonian,. Adiabatic approximation. Sudden approximation. Beginning of electron/field interaction. STATIONARY PERTURBATION THEORY 281 8. Rabi flopping analysis in the rotating wave approximation. 1 Time-independent nondegenerate perturbation theory General formulation First-order theory Second-order theory 2 Time-independent degenerate perturbation theory General formulation Example: Two-dimensional harmonic oscilator 3 Time-dependent perturbation theory 4 Literature Igor Luka cevi c Perturbation theory. Approximation Methods I. Several problems can be treated by the sudden perturbation theory: radiation of suddenly accelerated charge, atom excitation in neutron-nucleus collisions, atomic transitions while beta decay of nucleus. 18) y e-tsin is goodto order unity onthe interval oflength 1/e. The author use perturbation theory to derive the result $$T<<\hbar/\delta \overline{H}$$,when the Hamiltonian change over time T. Taylor series are extremely powerful tools for approximating functions that can be difficult to compute otherwise, as well as evaluating infinite sums and integrals by recognizing Taylor series. We also briefly describe Fermi's golden rule, the sudden approximation, and the creation of light from atomic hydrogen. Berry's phase. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. Time-independent perturbation theory Variational principles. With perturbation theory we can calculate just how small the gravitational effect within the hydrogen atom actually is. In slow-roll approximation and in longitudinal gauge, we find the primoradial perturbation spectrums for this scenario. Variational method, sudden approximation, time-independent perturbation theory. A perturbation series is written in powers of the parameter ωτ, which is small when the perturbation is "sudden"; ℏω is the typical eigenvalue of the unperturbed system; and τ is the. edu Report submitted to Prof. V(r)=0, 1/r, (1/r) 2 (fall to center). Atomic terms. With atomic orbitals as. 1 , with application to systems exposed to external magnetic and external electric fields, and then degenerate. [email protected] Because of the complexity of many physical problems, very few can be solved exactly (unless they involve only small Hilbert spaces). com/channel/UCmIchtf7_PvcAOfT5p5f6eQ Unacademy - https://unacademy. 1 , with application to systems exposed to external magnetic and external electric fields, and then degenerate. 2, including the WKB approximation in Sec. In particular, second- and third-order approximations are easy to compute and notably improve accuracy. The LaTeX Templates. The left graphic shows unperturbed (blue dashed. Idea General. Z to Z±1 is so small that perturbation theory is a good approximation. The Coulomb potential: hydrogen atom; Perturbation theory. Second-Order Time-Dependent Perturbation Theory Sudden perturbation. The process can be continued to third and higher orders. The Lorentz line‐shape expression is derived in the limit of low pressures, and explicit expressions for the frequency‐shift and linewidth parameters are given. (1995); Bernardeau et al. We also briefly describe Fermi's golden rule, the sudden approximation, and the creation of light from atomic hydrogen. If only concerned about the neighborhood very close to the origin, the n = 2 n=2 n = 2 approximation represents the sine wave sufficiently, and no. I am referring to original PDF by K. 221A Lecture Notes Time-Dependent Perturbation Theory 1 Introduction The time-independent perturbation theory is very successful when the system posses a small dimensionless parameter. Time-independent perturbation theory: nondegenerate and degenerate cases. Semiclassical approximation. Homework Statement In a beta decay H3 -> He3+, use the sudden perturbation approximation to determine the probability of that an electron initially in the 1s state of H3 will end up in the |n=16,l=3,m=0> state of He3+ Homework Equations | and |nlm> in spherical coordinates to calculate. The reader can ﬁnd a review on the subject in Bouchet et al. Consider the. TDPT: Time-dependent perturbation theory (Dirac); SA: Sudden approximation (Messiah); AA: Adiabatic approxima-tion (Born and Fock). Perturbation theory, quantum theory of radiation, radiative transitions Module 4 of Refresher course conducted by Indian Academies of Sciences at Bishop Moore College, Mavelikara, Kerala, May 5-17, 2014 Govind S. Looking for abbreviations of PT-MVD? It is Perturbation theory. First order time dependent perturbation theory under a harmonic perturbation. The philosophy behind singular perturbation theory is to take advantage of this separation of scales to obtain reduced problems that are simpler than the original full problem. Vibration and rotation spectra. We express the corresponding transition probabilities through the known inelastic atomic form factors widely used in the theory of relativistic. For example, perturbation theory can be used to approximately solve an anharmonic oscillator problem with the Hamiltonian (132) Here, since we know how to solve the harmonic oscillator problem (see 5. However, it is not capable of. Time Dependent Perturbation Theory. 1 Non-degenerate Case 282 8. TIME-DEPENDENT PERTURBATION THEORY 1. 1 , with application to systems exposed to external magnetic and external electric fields, and then degenerate. 18) y e-tsin is goodto order unity onthe interval oflength 1/e. - The collision model is exactly the same as the one used by Omont for the. Time-dependent perturbation theory 101 and then we can get bkEk +λ X n Wknbne −iEn−Ek ~ t = i~[dbk dt − i ~ Ekbk] (16) so we can get: dbk dt = λ i~ X n Wkne −i Ek− n ~ tb n (17) This is the exact equation which we didn't use any approximation, and this equation is equivalent to the Schrodinger equation. The LaTeX Templates. The author use perturbation theory to derive the result $$T<<\hbar/\delta \overline{H}$$,when the Hamiltonian change over time T. It allows us to work out corrections to the energy eigenvalues and eigenstates. III we review many. Time-Dependent Perturbation Theory 3. Ronald Castillon Says: April 21st, 2009 at 5:21 am. After the decay, the daughter system may be in the ground state, or in excited states. Beginning of electron/field interaction. 3 Solution for perturbation eq. Rotations and Angular Momentum (Sakurai ch 3). Motions in Resonant Zones in Nearly Integrable Systems 7. Vibration and rotation spectra. (Please follow all the calculations with pen and paper if this is your ﬁrst experience with perturbation theory. The main prediction of the present work is the presence of a. In this chapter we will discuss time independent perturbation theory. It is clear that the term(2. Penetration through (reflection from) a potential barrier. Introduce a small parameter ǫ writing the initial value as X + ǫZ, X′(t,ǫ) = F(X(t,ǫ)), X(0,ǫ) = X +ǫZ. It is clear that the term(2. View Test Prep - QM15-1 from PHYS 137 at University of California, Berkeley. Model of collision. The simpler quantum system is considered as being perturbed by weak physical disturbances, leading to a useful mathematical approximation for the original, more complicated system. Photons (Baym ch 1). perturbation theory, when modelling time domain seismic waveforms. Time Dependent Perturbation Theory. Given this interpretation, a perturbation methods ﬁnds a local approx-imation of the functions g and h. After the decay, the daughter system may be in the ground state, or in excited states. Time-dependent perturbation theory "Sudden" perturbation Harmonic perturbations: Fermi's Golden Rule. 254464 and 0. Unlike the traditional approach, it is not a perturbation theory based on an elastic trajectory. Semiclassical approximation methods are presented in Sec. Algebraic perturbation theory 1. Ask Question Time-dependent perturbation theory in a harmonic oscillator with a time-dependent force. Perturbation is used to find the roots of an algebraic equation that differs slightly from one for which the roots are known. Possible Topics. Motions in Resonant Zones in Nearly Integrable Systems 7. Non-degenerate perturbation theory. Perturbation Theory Our ﬁrst approach is to treat the Coulomb energy between two electrons as a pertur-bation on the original problem. Quantum and semiclassical treatment A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. A treatment, within the framework of the sudden perturbation approximation of time-dependent perturbation theory, of the pressure broadening of rotational transitions is presented. Fermann‡ and Scott M. In other words, the approximation is easier to use than the exact result. the harmonic oscillator, the quantum rotator, or the hydrogen atom. Oprea for Math 676, Fall 2010 Abstract. Rubin December 2, 2010 Lecture 32-41 November 10- December 3, 2010 1 Stationary state perturbation theory 1. Examples: in quantum field theory (which is in fact a nonlinear generalization of QM), most of the efforts is to develop new ways to do perturbation theory (Loop expansions, 1/N expansions, 4-ϵ expansions). For the Variational method approximation, the calculations begin with an uncorrelated wavefunction in which both electrons are placed in a hydrogenic orbital with scale factor $$\alpha$$. Selection rules 12. Perturbation Theory D. Nature of the Paper. Partial waves. 2, including the WKB approximation in Sec. Conclusions Acknowledgement Related Chapters Glossary Bibliography Biographical Sketch Summary The classical Hamiltonian perturbation theory (the name ―canonical perturbation theory‖ is also used) is a bridge between the general Hamiltonian dynamics and. Except in those few cases where one root is obvious (and hence the cubic can be reduced to a quadratic), cubic equations are nearly always solved in practice by a numerical or approximate method. Singular perturbation theory Marc R. Coupled cluster essentially takes the basic Hartree-Fock molecular orbital method and constructs multi-electron wavefunctions using. Time-dependent perturbation theory. In particular, second- and third-order approximations are easy to compute and notably improve accuracy. Concept Building Question 10 Part 2 (CSIR UGC Net Dec 2013) Degenerate Perturbation Theory. Sudden Changes 2. 2 Phenomenological theory of lattice dynamics Within the adiabatic approximation, the statics and dynamics of the ions are governed by an effective potential (R) = V ii(R)+E 0(R); (9) where E. Given this interpretation, a perturbation methods ﬁnds a local approx-imation of the functions g and h. The author use perturbation theory to derive the result $$T<<\hbar/\delta \overline{H}$$,when the Hamiltonian change over time T. Beginning of electron/field interaction. The adiabatic theorem is a concept in quantum mechanics. We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. Perturbation theory, quantum theory of radiation, radiative transitions Module 4 of Refresher course conducted by Indian Academies of Sciences at Bishop Moore College, Mavelikara, Kerala, May 5-17, 2014 Govind S. An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. Ercolani, C. orem for ordinary diﬀerential equations justiﬁes the computations of perturbation theory. 14) results from expansion of the exponential. edu Report submitted to Prof. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final. approximation is adequate for both free-electron-like systems and for compounds possessing tighter bound valence electrons like transition metals. Non-degenerate perturbation theory. Roussel October 19, 2005 1 Introduction When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. Supplementary subject: Quantum Chemistry Perturbation theory 6 lectures, (Tuesday and Friday, weeks 4-6 of Hilary term. A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. Detailed. Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. 2, including the WKB approximation in Sec. It may be the case, however, that a parameter can be identiﬁed, say ", such that. Such a contribution is completely invisible in perturbation theory. A perturbation series is written in powers of the parameter ωτ, which is small when the perturbation is "sudden"; ℏω is the typical eigenvalue of the unperturbed system; and τ is the. It's great. Fast-Changing Environment: Sudden Approximation; Slowly changing Environment: The Adiabatic Approximation (Reading for Fast Changing Environments: AMJ 37, 1969, AMJ_38_70_1970, AMJ_58_54_1990) 5. Suppose that y(t,ǫ) is the solution of an ordinary diﬀerential equation in which the equation and the initial data depend smoothly on a parameter ǫ. Perturbation theory will show , then, how the αi and βi will vary with a given perturbation. Lecture video files. (1995); Bernardeau et al. Acomparisonwiththe exact solution showsthat the approximation (2. 1 Time-independent nondegenerate perturbation theory General formulation First-order theory Second-order theory 2 Time-independent degenerate perturbation theory General formulation Example: Two-dimensional harmonic oscilator 3 Time-dependent perturbation theory 4 Literature Igor Luka cevi c Perturbation theory. Youtube Channel (Hindi) - https://www. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean field theory, density functional theory, multireference theory, and quantum Monte Carlo. Transition probability: Sudden approximation if the perturbation is large. ) 2 What is perturbation theory. Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. We then describe time-dependent phenomena in quantum mechanics, including time-ordered products, evolution operators, and perturbation theory. The 1-D harmonic oscillator, the sudden approximation, time-dependent perturbation theory; Reasoning: The system is a 1-D harmonic oscillator. Like the standard. Find the exact expression for the energy and then use perturbation theory to calculate the same. azimutal close coupled-infinite order sudden approximate double substitution coupled cluster method approximate coupled cluster with double excitations polarization propagator approximation adiabatic capture + global centrifugal sudden approximation (theory for association and ion-molecule reactions without energetic barriers) - T. In this example we will show the relative energy shift between the unperturbed 1s state and the corrected 1s state due to the gravitational potential between the proton and the electron in atomic hydrogen. The tritium nucleus undergoes beta decay such that (1) 3H +3 Hete +ve Using the sudden approximation in perturbation theory, calculate the probability that the resulting 3He+ ion is in each of the 1s 2s 2p states. x5 16x+1 = 0: (1) For the reference, Eq. Scattering theory (Chapter 11) • Meaning of Cross-Section • Partial wave analysis and phase shifts • The Born approximation. formula allows one to calculate the transition probabilities under the action of sudden perturbations which are small in absolute value whenever perturbation theory is applicable. In the section on time-independent perturbation theory in the Chapter on approximation methods we did not speciﬁcally designate the coor-dinates. The process can be continued to third and higher orders. Born-Oppenheimer approximation. While the string perturbation series is a well-defined expression analogous to the Feynman perturbation series, by itself it lacks a conceptual property of the latter: the Feynman perturbation series is known, in principle, to be the approximation to something, namely to the corresponding complete hence non-perturbative quantum field theory. is V^ (0) k +H^0 (1) k = E (1) k k +E 0) k k or, using the zero-order results V^ E(1) k k = ek H^0 (1) k By the completeness principle, we can always express (1) k in. We will apply time-dependent perturbation theory, during this course, to the problem of emission and absorption of radiation and also to scattering problems. the harmonic oscillator, the quantum rotator, or the hydrogen atom. de Cuyo, 8400 Bariloche, Argentina. approximation techniques. Perturbation, in mathematics, method for solving a problem by comparing it with a similar one for which the solution is known. The Helium ground state has two electrons in the 1s level. The equations of string theory are incredibly complex, so they often can only be solved through a mathematical method of approximation called perturbation theory. Phase shifts. Singular perturbation theory Marc R. The Perturbation is also assumed to be instantaneous and time dependent such that sudden approximation can be applied in the time evolution of states. Faced with a problem that we cannot solve exactly, but that is close (in some sense) to an auxiliary problem that we can solve exactly, a. a perfect approximation for any value zno matter how far away from z. Time-dependent potentials: general formalism Time-dependent perturbation theory “Sudden” perturbation Harmonic perturbations: Fermi’s Golden Rule. Semiclassical approximation. Possible Topics. First-order ground state perturbation theory There are not many quantum problems that can be solved exactly, so approximation methods are very important. : 1st-order Now consider the solution to the above sequence of the perturbation eqs. The project is an investigation of multiple timescale perturbation theory applied to solving the van der Pol oscillator. 1 Time-independent nondegenerate perturbation theory General formulation First-order theory Second-order theory 2 Time-independent degenerate perturbation theory General formulation Example: Two-dimensional harmonic oscilator 3 Time-dependent perturbation theory 4 Literature Igor Luka cevi c Perturbation theory. 1 An introductory example The quadratic equation x2 −πx+2 = 0, (1. A particle is in its ground state in the left well. Time-Dependent Perturbation Theory. The validity of the perturbation approximation for rough surface scattering is examined (1) by comparison with exact results obtained by solving an integral equation and (2) through comparison of low‐order perturbation predictions with higher‐order predictions. Substituting we get the approximation The exact solution, up to 9 decimal places, is -1. View Homework Help - QM14 from PHYSICS 137 at University of California, Berkeley. Semiclassical approximation. Semiclassical approximation methods are presented in Sec. Several problems can be treated by the sudden perturbation theory: radiation of suddenly accelerated charge, atom excitation in neutron-nucleus collisions, atomic transitions while beta decay of nucleus. While the string perturbation series is a well-defined expression analogous to the Feynman perturbation series, by itself it lacks a conceptual property of the latter: the Feynman perturbation series is known, in principle, to be the approximation to something, namely to the corresponding complete hence non-perturbative quantum field theory. After the decay, the daughter system may be in the ground state, or in excited states. Oprea for Math 676, Fall 2010 Abstract. This handout details the steps in perturbation computations. theory is the most useful approximation setup, but we will also consider the adiabatic and sudden approximations. Brief introduction to perturbation theory 1. In ordinary perturbation theory, a perturbation is expressed mathematically by a perturbed Hamiltonian in the Schrodinger equation describ-¨ ing the whole system 4,5wx. An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. Pertubation Theory/Asymptotic Analysis is an important subject in applied mathematics, and there are many techniques used in this study, one of which. Perturbation Theory Up: quantrev Previous: The Hydrogen Atom Contents Approximate Methods The problems discussed in the previous section (harmonic oscillator, rigid rotator, etc. 12:09 mins. Spontaneous Emission Up: Time-Dependent Perturbation Theory Previous: Electromagnetic Radiation Electric Dipole Approximation In general, the wavelength of the type of electromagnetic radiation which induces, or is emitted during, transitions between different atomic energy levels is much larger than the typical size of an atom. Since the spatial state is symmetric, the spin part of the state must be antisymmetric so (as it always is for closed shells). 6) Sudden approximation Adiabatic approximation Time-dependent perturbation theory Schrodinger, Heisenberg, Interaction pictures Dyson series for time-evolution operator in Interaction picture 1st order solution to time-dependent perturbation theory (transition coe cients) FERMI. We express the corresponding transition probabilities through the known inelastic atomic form factors widely used in the theory of relativistic. • If Hˆ 0 is compatible with Vˆ, i. Beginning of electro. In particular, second- and third-order approximations are easy to compute and notably improve accuracy. I am reading quantum mechanics (Messiah) now. Possible Topics.  General problem. Radiative transitions. The Lorentz line‐shape expression is derived in the limit of low pressures, and explicit expressions for the frequency‐shift and linewidth parameters are given. 1 Introduction So far we have concentrated on systems for which we could ﬁnd exactly the eigenvalues and eigenfunctions of the Hamiltonian, like e. Nature of the Paper. Fast-Changing Environment: Sudden Approximation; Slowly changing Environment: The Adiabatic Approximation (Reading for Fast Changing Environments: AMJ 37, 1969, AMJ_38_70_1970, AMJ_58_54_1990) 5. The purpose of this Module is to examine five trial wavefunctions for the helium atom used within the Perturbation Theory and Variational method approximation. Many-Body Perturbation Theory The GW approximation C. edu Report submitted to Prof. Approximation Techniques in Time-Dependent Problems In this chapter, I discuss some general techniques that can be used to obtain approximate solutions to time-dependent problems in quantum mechanics. Time Dependent Perturbation ( When Perturbation is Constant) Adiabatic and Sudden Approximation Part 2 (please multiply 4 in Nr and w_fi^4 in Dr in eq. Bound states: Bohr-Sommerfeld quantization rule. 3 presents perturbation theory, starting with time-independent nondegenerate perturbation theory in Sec. Abstract The sudden approximation for rotational excitation of diatomic polar molecules by atomic impact is applied, yielding semiclassical angular distributions of rotational transition cross sections and their energy dependence. An explicit expression using a harmonic oscillator model is given for the vibrational progression k′ ← 0″, where k′, 0″ are the vibrational quantum numbers in the final. Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. We have to split the hamiltonian into two parts. Given this interpretation, a perturbation methods ﬁnds a local approx-imation of the functions g and h. According to the Pauli principle, however, the wave function of the system must be antisymmetrie with. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Ronald Castillon Says: April 21st, 2009 at 5:21 am. Time-dependent perturbation theory So far, we have focused on quantum mechanics of systems described by Hamiltonians that are time-independent. Time-Dependent Perturbation Theory 3. Time-independent perturbation theory Introduction As discussed in Lecture notes 14, relatively few problems in quantum mechanics are exactly solvable. Perturbation theory in quantum mechanics provides an approximation scheme whereby the physical properties of a system, modeled mathematically by a quantum-mechanical description, can be estimated to a required degree of accuracy. If we move the support 'quickly', the motion of the bob will be wildly chaotic. In particular, second- and third-order approximations are easy to compute and notably improve accuracy. V(r)=0, 1/r, (1/r) 2 (fall to center). Because of the complexity of many physical problems, very few can be solved exactly (unless they involve only small Hilbert spaces). Partial waves. Perturbation theory, quantum theory of radiation, radiative transitions Module 4 of Refresher course conducted by Indian Academies of Sciences at Bishop Moore College, Mavelikara, Kerala, May 5-17, 2014 Govind S. Lecture Notes for PHY851/852. Fast-Changing Environment: Sudden Approximation; Slowly changing Environment: The Adiabatic Approximation (Reading for Fast Changing Environments: AMJ 37, 1969, AMJ_38_70_1970, AMJ_58_54_1990) 5. TIME-DEPENDENT PERTURBATION THEORY 1. This form for the state vector suggests that the inverse (or adjoint) operator U+ acts on the fully-evolving state vector of the Schrödinger picture to "back out" or undo the fast evolution associated with. The two courses together are intended to provide an introduction to quantum mechanics. This form for the state vector suggests that the inverse (or adjoint) operator U+ acts on the fully-evolving state vector of the Schrödinger picture to “back out” or undo the fast evolution associated with. The rst few terms of a perturbation series are called a perturbation solution or approximation. Concept Building Question 11 (CSIR UGC NET DEC 2015) Part 1 Introduction to Adiabatic and Sudden Approximation (Transition Probability) Learn Complete Quantum Mechanics and Classical Mechanics Live In Unacademy Plus. 2nd order perturbation theory If we carry out the perturbation theory to the next order of approximation, one further iteration of Eq. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean field theory, density functional theory, multireference theory, and quantum Monte Carlo. Fermi golden rule. And we suppose that there is no. A sudden perturbation is defined here as a sudden switch from one time-independent Hamiltonian to another one , the time of switching being much shorter than any natural period of the system. k ±perturbation). Because of the complexity of many physical problems, very few can be solved exactly (unless they involve only small Hilbert spaces). com/channel/UCmIchtf7_PvcAOfT5p5f6eQ Unacademy - https://unacademy. In other words, the approximation is easier to use than the exact result. Effects of kinesio tape compared with nonelastic sports tape and the untaped ankle during a sudden inversion perturbation in male athletes. Keywords: sudden approximation, inﬁnite potential well, scattering states 1. Algebraic perturbation theory 1. A treatment, within the framework of the sudden perturbation approximation of time-dependent perturbation theory, of the pressure broadening of rotational transitions is presented. Nature of the Paper. de Energ´ıa Atomica and Univ. Pertubation Theory/Asymptotic Analysis is an important subject in applied mathematics, and there are many techniques used in this study, one of which. Z47 2009 530. Some remarks on approximation methods for quantum systems in higher space dimensions we apply degenerate perturbation theory to perturbed N-dimensional inﬁnite cubical well. The validity of the perturbation approximation for rough surface scattering is examined (1) by comparison with exact results obtained by solving an integral equation and (2) through comparison of low‐order perturbation predictions with higher‐order predictions. Motions in Resonant Zones in Nearly Integrable Systems 7. Decoherence, measurement and Bell's inequalities. No particular significance is attached to the way that material is divided between the two courses. A treatment, within the framework of the sudden perturbation approximation of time‐dependent perturbation theory, of the pressure broadening of rotational transitions is presented. At every cosmologically interesting scale, it aptly and succesfully describes the situation in the early eons after the decoupling of radiation and matter at recombination. The tritium nucleus undergoes beta decay such that (1) 3H +3 Hete +ve Using the sudden approximation in perturbation theory, calculate the probability that the resulting 3He+ ion is in each of the 1s 2s 2p states. Calculate the rst order perturbation in the energy for n-th state of a 1-dim harmonic oscillator subjected to perturbation x4, is a constant. In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. Approximation Techniques in Time-Dependent Problems In this chapter, I discuss some general techniques that can be used to obtain approximate solutions to time-dependent problems in quantum mechanics. Consider, for example, an ideal pendulum, with no friction or air resistance, oscillating back and forth in a vertical plane. A sudden perturbation is defined here as a sudden switch from one time-independent Hamiltonian to another one , the time of switching being much shorter than any natural period of the system. Time dependent perturbation theory Sudden approximation Adiabatic approximation Time-dependent perturbation theory Schrodinger, Heisenberg, Interaction pictures Dyson series for time-evolution operator in Interaction picture 1st order solution to time-dependent perturbation theory (transition coe cients) FERMI GOLDEN RULE Monochromatic case. Rotations and Angular Momentum (Sakurai ch 3). The pressure release boundary condition is assumed, and the field quantity calculated is the bistatic scattering cross section. We express the corresponding transition probabilities through the known inelastic atomic form factors widely used in the theory of relativistic. A treatment, within the framework of the sudden perturbation approximation of time‐dependent perturbation theory, of the pressure broadening of rotational transitions is presented. Vibration and rotation spectra. Hence, we can use much of what we already know about linearization. Variational method, sudden approximation, time-independent perturbation theory. 3) that the horizon now about √ 3 ×11. Mixed States and the Density Matrix (if time permits). I do not know if this book was translated. In this example we will show the relative energy shift between the unperturbed 1s state and the corrected 1s state due to the gravitational potential between the proton and the electron in atomic hydrogen. Perturbation theory, quantum theory of radiation, radiative transitions Module 4 of Refresher course conducted by Indian Academies of Sciences at Bishop Moore College, Mavelikara, Kerala, May 5-17, 2014 Govind S. The time-independent perturbation theory is very successful when the system posses a small dimensionless parameter. Time Dependent Perturbation Theory (When Perturbation is Time to Dependent) 10m 25s. Centrally Symmetric Fields. We will find out how the new perturbation affects the time evolution of electromagnetic field. The project is an investigation of multiple timescale perturbation theory applied to solving the van der Pol oscillator. approximation is adequate for both free-electron-like systems and for compounds possessing tighter bound valence electrons like transition metals. Rabi flopping analysis in the rotating wave approximation. Two-state approximation in the adiabatic and sudden-perturbation limits Article (PDF Available) in Physical Review A 18(5) · November 1978 with 151 Reads How we measure 'reads'. In addition, if we write Ek. If the system is initially in the vibrational stationary state m this means that a m ( t ) stays close to unity and a n ( t ), n ≠ m , close to zero. Scattering theory (Chapter 11) • Meaning of Cross-Section • Partial wave analysis and phase shifts • The Born approximation. As i read in your article this time, i didn't expect that the nature and equations of the theory will goes like that. Several problems can be treated by the sudden perturbation theory: radiation of suddenly accelerated charge, atom excitation in neutron-nucleus collisions, atomic transitions while beta decay of nucleus. In such cases, the time depen-dence of a wavepacket can be developed through the time-evolution operator, Uˆ = e−iHt/ˆ ! or, when cast in terms of the eigenstates of the Hamiltonian,. Approximation Techniques in Time-Dependent Problems In this chapter, I discuss some general techniques that can be used to obtain approximate solutions to time-dependent problems in quantum mechanics. Martin but I will put the necessary equations below. perturbation theory for intermolecular forces implies the necessity of defining an unperturbed state which is formed by the molecules sepa rately, and an interaction operator between the electrens and nuclei belonging to different molecules. Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. Perturbation is used to find the roots of an algebraic equation that differs slightly from one for which the roots are known. The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. And I get confused about the condition for the validity of the sudden approximation in CH. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbation" parts. The 1-D harmonic oscillator, the sudden approximation, time-dependent perturbation theory; Reasoning: The system is a 1-D harmonic oscillator. 254464 and 0. Possible Topics. PERTURBATION THEORY AND OPTIMALITY CONDITIONS FOR THE BEST MULTILINEAR RANK APPROXIMATION OF A TENSOR∗ LARS ELDEN´ † AND BERKANT SAVAS‡ Abstract. Pertubation Theory/Asymptotic Analysis is an important subject in applied mathematics, and there are many techniques used in this study, one of which. Introduction to Scattering Theory Statement of the problem: Scattering theory is essentially time-independent perturbation theory applied to the case of a continuous spectrum. A particle in an infinite square well, the sudden approximation; Reasoning: The sudden approximation can be used to calculate transition probabilities when the Hamiltonian changes rapidly. A perturbation series is an analytic guess for a solution of the form y 0(t) + y 1(t) + 2y 2(t) + : The basic idea of the regular perturbation method is to substitute this guess into the equation and solve for y 0(t), y 1(t), y 2(t), etc. ★ This looks like second order perturbation theory but is more general since the coupling of the ,a' space functions via the perturbing operator H1 is taken into account. k ±perturbation). What is the probability of finding the particle in the first excited state of the new well?. com/user/Sethi Disclaimer The information pr. 3 presents perturbation theory, starting with time-independent nondegenerate perturbation theory in Sec. Perturbation theory, quantum theory of radiation, radiative transitions Module 4 of Refresher course conducted by Indian Academies of Sciences at Bishop Moore College, Mavelikara, Kerala, May 5-17, 2014 Govind S. Sketch the ground state wavefunction and the correction, showing that the particle is more localised around the minimum of the potential. Like the standard. A particle is in its ground state in the left well. 2nd order perturbation theory If we carry out the perturbation theory to the next order of approximation, one further iteration of Eq. There are many such techniques developed over years, but these two are among the simplest, most fundamental, and most widely applied. KAM Theory 6. Interactions of atoms with classical electromagnetic ﬁelds. In particular, second- and third-order approximations are easy to compute and notably improve accuracy. Perturbation theory lets us find corrections to an exactly solvable problem when there is a small additional contribution to the potential. Perturbation theory in quantum mechanics provides an approximation scheme whereby the physical properties of a system, modeled mathematically by a quantum-mechanical description, can be estimated to a required degree of accuracy. And I get confused about the condition for the validity of the sudden approximation in CH. Indeed, 1st order perturbation theory gives a term of the form br s in this series. Such a scheme is useful because very few problems occurring in quantum mechanics can be solved analytically. In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. 1 Non-degenerate case. Sudden perturbations. The Lorentz line‐shape expression is derived in the limit of low pressures, and explicit expressions for the frequency‐shift and linewidth parameters are given. General formalism. Krishnaswami, Chennai Mathematical Institute These are very brief and incomplete notes for lectures at the above Refresher Course. The other ingredient needed for this reduction is the transforma-tion of the conventional set of variables to action-angle variables. Suppose that the perturbation turns on suddenly at time t= t0 = 0, and is constant thereafter: H1(t)=H ~ (t); (5) Within the rotating-wave approximation, the results of this section still hold with. However, it is not capable of working out consequences of a perturbation that depends on time. Introduce a small parameter ǫ writing the initial value as X + ǫZ, X′(t,ǫ) = F(X(t,ǫ)), X(0,ǫ) = X +ǫZ. Sketch the ground state wavefunction and the correction, showing that the particle is more localised around the minimum of the potential. repeated Silas, in a sudden perturbation. He continues with approximation methods, perturbation theory, quanta in crystalline materials, various matrices, perturbation quantity; Perturbation theory; Perturbation theory (quantum mechanics). , $$\langle k\rangle \gg 1$$, the expansion parameter ε is small, and it is expected that the perturbation theory yields reasonable approximation of. Hence, we can use much of what we already know about linearization. Perturbation theory (in quantum mechanics) is a set of approximation schemes for reducing the mathematical analysis of a complicated quantum system to a simpler mathematical solution. We then describe time-dependent phenomena in quantum mechanics, including time-ordered products, evolution operators, and perturbation theory. The task of perturbation theory is to approximate the energies and wavefunctions of the perturbed system by calculating corrections up to a given order. We discussed a simple application of the perturbation technique previously with the Zeeman effect. com/channel/UCmIchtf7_PvcAOfT5p5f6eQ Unacademy - https://unacademy. If we neglect the term, we still get a decent approximation: Perturbation theory is useful only if you are looking for the root of the perturbed equation that falls near the root of the unperturbed equation (). 1 An example of perturbative analysis: roots of a polynomial We consider ﬁrst an elementary example to introduce the ideas of regular perturbation theory. Symmetry of the hydrogen atom, Lenz's vector, etc (Baym ch 7). ★ We could have arrived at this result as well by a formal series expansion of the inverse matrix that would then also deﬁne higher order corrections to the eﬀective. The Course Outlines and syllabi on this web page represent the best descriptions of some of the graduate courses that are available at this time. Perturbation theory will show , then, how the αi and βi will vary with a given perturbation. 1 Non-degenerate Case 282 8. However, it is not capable of working out consequences of a perturbation that depends on time. Spontaneous Emission Up: Time-Dependent Perturbation Theory Previous: Electromagnetic Radiation Electric Dipole Approximation In general, the wavelength of the type of electromagnetic radiation which induces, or is emitted during, transitions between different atomic energy levels is much larger than the typical size of an atom. 1 Band Theory and Effective Masses 288 8. 8:51 mins. When the network is sufficiently dense, i. Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. In particular, second- and third-order approximations are easy to compute and notably improve accuracy. II we review the adiabatic approximation, highlight-ing the conditions that the snapshot eigenvectors and eigenvalues of H(t) must satisfy for this approximation to be valid. 1363v2 [quant-ph] 19 Nov 2009 Beyond theQuantum Adiabatic Approximation: Adiabatic Perturbation Theory Gustavo Rigolin,1, ∗ Gerardo Ortiz,1, † and V´ıctor Hugo Ponce2 1Department of Physics, Indiana University, Bloomington, IN 47405, USA 2Centro Atomico Bariloche and Instituto Balseiro, Com. Perturbation theory, quantum theory of radiation, radiative transitions Module 4 of Refresher course conducted by Indian Academies of Sciences at Bishop Moore College, Mavelikara, Kerala, May 5-17, 2014 Govind S. Before proceeding, there is a question that we should always ask in perturbation theory: what is the small, dimensionless parameter that ensures that the additional term is smaller than the original terms?. 50,60 This transformation is required by classical perturbation theory and is the limiting step in the current approach. Time-Dependent Perturbation Theory 3. Time-dependent perturbation theory 101 and then we can get bkEk +λ X n Wknbne −iEn−Ek ~ t = i~[dbk dt − i ~ Ekbk] (16) so we can get: dbk dt = λ i~ X n Wkne −i Ek− n ~ tb n (17) This is the exact equation which we didn't use any approximation, and this equation is equivalent to the Schrodinger equation. Time Dependent Perturbation Theory. Detailed. Note that the perturbation due to the repulsion between the two electrons is about the same size as the the rest of the Hamiltonian so first order perturbation theory is unlikely to be accurate. The purpose of this Module is to examine five trial wavefunctions for the helium atom used within the Perturbation Theory and Variational method approximation. 1 Non-degenerate case. The other ingredient needed for this reduction is the transforma-tion of the conventional set of variables to action-angle variables. Consider the. A sudden perturbation is defined here as a sudden switch from one time-independent Hamiltonian H 0 to another one H perturbation theory is irrelevant: The first-order approximation to keep the vector c i = 1,. Beginning of electro. Symmetry of the hydrogen atom, Lenz's vector, etc (Baym ch 7). In addition, if we write Ek. Recently, perturbation methods have been gaining much popularity. 2 Van der Waals Interactions 295 VARIATIONAL METHOD 298 8. 1 Nondegenerate Formalism We have a Hamiltonian H= H 0 + V and we suppose that we have determined the complete set of solutions to H 0 with ket jn 0iso that H 0jn 0i= E0 n jn 0i. Interactions of atoms with classical electromagnetic ﬁelds. Perturbation theory, quantum theory of radiation, radiative transitions Module 4 of Refresher course conducted by Indian Academies of Sciences at Bishop Moore College, Mavelikara, Kerala, May 5-17, 2014 Govind S. However, we should. A treatment, within the framework of the sudden perturbation approximation of time-dependent perturbation theory, of the pressure broadening of rotational transitions is presented. 1 Non-degenerate case. Substituting we get the approximation The exact solution, up to 9 decimal places, is -1. Krishnaswami, Chennai Mathematical Institute These are very brief and incomplete notes for lectures at the above Refresher Course. The author use perturbation theory to derive the result $$T<<\hbar/\delta \overline{H}$$,when the Hamiltonian change over time T. 221A Lecture Notes Time-Dependent Perturbation Theory 1 Introduction The time-independent perturbation theory is very successful when the system posses a small dimensionless parameter. This approximation drops terms higher order in δX. A Sudden Approximation via Semiclassical Rate Theory† Justin T. Beware! These are in a pretty crude format. Time-independent perturbation theory: nondegenerate and degenerate cases. 50,60 This transformation is required by classical perturbation theory and is the limiting step in the current approach. Suppose that y(t,ǫ) is the solution of an ordinary diﬀerential equation in which the equation and the initial data depend smoothly on a parameter ǫ. However, it is not capable of. Approximation Techniques in Time-Dependent Problems In this chapter, I discuss some general techniques that can be used to obtain approximate solutions to time-dependent problems in quantum mechanics. A particle is in its ground state in the left well. Multistate Complete-Active-Space Second-Order Perturbation Theory Based on Density Matrix Renormalization Group Reference States Takeshi Yanai,*,†,‡ Masaaki Saitow,‡, Xiao-Gen Xiong,§ Jakub Chalupsky,́∥ Yuki Kurashige,⊥,∇ Sheng Guo,# and Sandeep Sharma †Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, 444-8585 Aichi Japan. Born Approximation.  General problem. It is used in the study of PDEs involving operators depending on small parameter, in classical and celestical. Rotating wave approximation. METHOD The project used Maple - the symbolic mathematical language, version 15. By a local approximation, we mean an approximation that is valid in the neighborhood of a particular point (¯x,σ¯). Sudden Changes 2. Why might we prefer the approximation (1. In such cases, the time depen-dence of a wavepacket can be developed through the time-evolution operator, Uˆ = e−iHt/ˆ ! or, when cast in terms of the eigenstates of the Hamiltonian,. No particular significance is attached to the way that material is divided between the two courses. In this example we will show the relative energy shift between the unperturbed 1s state and the corrected 1s state due to the gravitational potential between the proton and the electron in atomic hydrogen. In general, there’s no panacea, no universal solution to all problems in quantum mechanics. Z to Z±1 is so small that perturbation theory is a good approximation. Perturbation Theory Up: quantrev Previous: The Hydrogen Atom Contents Approximate Methods The problems discussed in the previous section (harmonic oscillator, rigid rotator, etc. Motion in central potential. Moloney, for a summer school held in Cork, Ireland, from 1994 to 1997. Brief introduction to perturbation theory 1. Rotating wave approximation. That means that we know there is an eigenstate of the full Hamiltonian for every possible energy, E. (B) RHS ) 15m 00s. It may be the case, however, that a parameter can be identiﬁed, say ", such that. The links below will take you to online overviews of some of the concepts used here. I am reading quantum mechanics (Messiah) now. We express the corresponding transition probabilities through the known inelastic atomic form factors widely used in the theory of relativistic. Transition probability: Sudden approximation if the perturbation is large. By this way we can solve the problems with a very good approximation. , $$\langle k\rangle \gg 1$$, the expansion parameter ε is small, and it is expected that the perturbation theory yields reasonable approximation of. 24) in which we have substituted for the an coe-cient in Eq. Perturbation Theory and the WKB Method Jaime Shinn Department of Mathematics Colorado State University [email protected] Ask Question The task is then to use perturbation theory to show that the second-order approximation to the solution to this DE is: By starting point is to use the theory for a regular perturbation (since the modulus of $\epsilon$ is much less than $1$). The tritium nucleus undergoes beta decay such that (1) 3H +3 Hete +ve Using the sudden approximation in perturbation theory, calculate the probability that the resulting 3He+ ion is in each of the 1s 2s 2p states. Hence, we can use much of what we already know about linearization. The links below will take you to online overviews of some of the concepts used here. Recently, perturbation methods have been gaining much popularity. In simpler terms, a quantum mechanical system subjected to gradually changing external conditions adapts its functional form, but when subjected to rapidly varying conditions there is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged. A Comparison of Perturbation Theory and the Small-Slope Approximation for Acoustic Scattering From a Rough Interf ace for a Biot Medium T aiqian Y ang, Shira L ynn Broschat ,Senior Member ,IEEE ,and Cristina Galea AbstractÑ In this paper , the lowest order small-slope appr ox-imation (SSA) scattering cr oss section for Biot theory is deri ved. This handout details the steps in perturbation computations. As i read in your article this time, i didn't expect that the nature and equations of the theory will goes like that. A “Sudden” Perturbation A sudden perturbation is defined here as a sudden switch from one time-independent Hamiltonian H 0 to another one H ′ 0 , the time of switching being much shorter than any natural period of the system. An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. The five quantum operator identities: (i) Leibnitz, (ii) Hadamard, (iii) Baker-Campbell-Hausdorff, (iv) exponential reordering (braiding. PT-MVD - Perturbation theory. formula allows one to calculate the transition probabilities under the action of sudden perturbations which are small in absolute value whenever perturbation theory is applicable. The main prediction of the present work is the presence of a. Perturbation theory is applicable if the problem at hand cannot be solved exactly, but can be formulated by. • Approximation methods in quantum mechanics, review of non-degenerate perturbation theory, degenerate perturbation theory, time dependent perturbation theory, periodic perturbation, Rabbi flopping frequency, Adiabatic approximation, Berry phase, sudden approximation [5 lectures] • Interaction of quantum systems with radiation, Dipole. For the pure rotational case, the theory reduces to a sudden approximation superior to the current alternatives. The main prediction of the present work is the presence of a. We discussed a simple application of the perturbation technique previously with the Zeeman effect. The pressure release boundary condition is assumed, and the field quantity calculated is the bistatic scattering cross section. Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. We can do that as follows. We will find out how the new perturbation affects the time evolution of electromagnetic field. Syllabus for Physics 506: Quantum Mechanics II Spring 2020. Perturbation theories is in many cases the only theoretical technique that we have to handle various complex systems (quantum and classical). ★ This looks like second order perturbation theory but is more general since the coupling of the ,a' space functions via the perturbing operator H1 is taken into account. Scattering and Identical Particles. Scattering Theory 9. The other ingredient needed for this reduction is the transforma-tion of the conventional set of variables to action-angle variables. We solve the Dirac equation describing the behavior of a hydrogen-like atom interacting with a spatially inhomogeneous ultrashort electromagnetic field pulse in the sudden-perturbation approximation. Rotations and Angular Momentum (Sakurai ch 3). In general, there’s no panacea, no universal solution to all problems in quantum mechanics. A “Sudden” Perturbation A sudden perturbation is defined here as a sudden switch from one time-independent Hamiltonian $$H_0$$ to another one $$H′_0$$, the time of switching being much shorter than any natural period of the system. 1 Lagrangian perturbation theory formalism Let us summarize the result of the Lagrangian perturbation theory. 1 Non-degenerate case. Sudden approximation. Interesting links. Z to Z±1 is so small that perturbation theory is a good approximation. It is clear that the term(2. Lecture Notes 1: Equivalent descriptions, time reversal invariance (updated 1/28/13) Lecture Notes 2: Approximation methods for bound states: variational method, time-independent non-degenerate perturbation theory, time-independent degenerate perturbation theory (updated 2/11/13) Lecture Notes 3: Time-dependent perturbation theory, sudden approximation, adiabatic approximation, harmonic. Beware! These are in a pretty crude format. Detailed. We have to split the hamiltonian into two parts. No particular significance is attached to the way that material is divided between the two courses. The Lorentz line‐shape expression is derived in the limit of low pressures, and explicit expressions for the frequency‐shift and linewidth parameters are given in terms of the intermolecular potential. Possible Topics. Semiclassical approximation. According to the Pauli principle, however, the wave function of the system must be antisymmetrie with. degenerate perturbation theory, time-independent degenerate perturbation theory. Time-dependent perturbation theory. The reader can ﬁnd a review on the subject in Bouchet et al. Time-dependent potentials: general formalism. Coupled cluster (CC) is a numerical technique used for describing many-body systems. We will find out how the new perturbation affects the time evolution of electromagnetic field. This handout details the steps in perturbation computations. It allows us to work out corrections to the energy eigenvalues and eigenstates. This form for the state vector suggests that the inverse (or adjoint) operator U+ acts on the fully-evolving state vector of the Schrödinger picture to “back out” or undo the fast evolution associated with. Effects of kinesio tape compared with nonelastic sports tape and the untaped ankle during a sudden inversion perturbation in male athletes. It uses both the elastic scattering from the spherically averaged potential and the infinite-order sudden (IOS) approximation as the unperturbed solutions. Penetration through (reflection from) a potential barrier. If we move the support 'quickly', the motion of the bob will be wildly chaotic. Geometric phases. This method is used in quantum mechanics and quantum field theory all the time and is a well-established mathematical process. Usually the solution found in this way is only approximate. In this method, physicists arrive at a first-order approximation, which is …. orem for ordinary diﬀerential equations justiﬁes the computations of perturbation theory. 1 Lagrangian perturbation theory formalism Let us summarize the result of the Lagrangian perturbation theory. PERTURBATION THEORY 17.  General problem. Perturbation theory, quantum theory of radiation, radiative transitions Module 4 of Refresher course conducted by Indian Academies of Sciences at Bishop Moore College, Mavelikara, Kerala, May 5-17, 2014 Govind S. Review of spin operators, Pauli matrices, and Pauli matrix identities. Introduction Because of the difﬁculty in solving the time-dependent Schrödinger equation (SE), people have proposed many intuitive theories to discuss the evolution of the wavefunction, which include the perturbation theory, adiabatic theorem and sudden approximation. • Approximation methods in quantum mechanics, review of non-degenerate perturbation theory, degenerate perturbation theory, time dependent perturbation theory, periodic perturbation, Rabbi flopping frequency, Adiabatic approximation, Berry phase, sudden approximation [5 lectures] • Interaction of quantum systems with radiation, Dipole. Lecture 1: January 8, 2020. A sudden perturbation is defined here as a sudden switch from one time-independent Hamiltonian to another one , the time of switching being much shorter than any natural period of the system. Z to Z±1 is so small that perturbation theory is a good approximation. After the decay, the daughter system may be in the ground state, or in excited states. Lecture 1: Time Independent Perturbation Theory. 1 Time-independent perturbation. Such a contribution is completely invisible in perturbation theory. k ±perturbation). III we review many. ISBN 978--470-02678-6 (cloth : alk. Time-independent perturbation theory is used when one wishes to nd energy eigenstates and the corresponding energy levels for a system for which the Hamiltonian H. Introduce a small parameter ǫ writing the initial value as X + ǫZ, X′(t,ǫ) = F(X(t,ǫ)), X(0,ǫ) = X +ǫZ. Download Course Materials. It is clear that the term(2. 221A Lecture Notes Time-Dependent Perturbation Theory 1 Introduction The time-independent perturbation theory is very successful when the system posses a small dimensionless parameter. Unlike the traditional approach, it is not a perturbation theory based on an elastic trajectory. Nature of the Paper. Several problems can be treated by the sudden perturbation theory: radiation of suddenly accelerated charge, atom excitation in neutron-nucleus collisions, atomic transitions while beta decay of nucleus. A -rst-order perturbation theory and linearization deliver the same output. 50,60 This transformation is required by classical perturbation theory and is the limiting step in the current approach. It is found that the energy difference for splitting decreases as N increases and it vanishes in the inﬁnite dimensional space. each degenerate. 12) fails to be uniformly valid. The usual one made in time-dependent perturbation theory is to suppose that H′ − H″ is so small that a n (t) stays close to its value at t = 0. Like the standard. Consider the. PT-MVD - Perturbation theory. APPROXIMATION METHODS IN QM 3. Sketch the ground state wavefunction and the correction, showing that the particle is more localised around the minimum of the potential. If we move the support 'quickly', the motion of the bob will be wildly chaotic. 1 Lagrangian perturbation theory formalism Let us summarize the result of the Lagrangian perturbation theory.
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# AP Statistics : How to identify sources of bias in a survey

## Example Questions

### Example Question #1 : How To Identify Sources Of Bias In A Survey

To find the percentage of households in a town who own more than one motor vehicle, a survey will ask the next 100 drivers at a popular gas station if there is more than one motor vehicle in their household. Is this survey biased and if so, what is the main type of bias?

Yes, voluntary response bias

None of the other answers are correct

Yes, undercoverage bias

Yes, non-response bias

No, the survey is representative of the local population

Yes, undercoverage bias

Explanation:

Because the survey is being conducted on drivers at a gas station, people/households who do not own a motor vehicle will not be included in the survey.

### Example Question #2 : How To Identify Sources Of Bias In A Survey

Identify the type of bias:

A researcher wants to know what proportion of coffee drinkers would pay more than $5 for a coffee drink. The researcher asks the following question: "Do you agree that$5 is way too much to pay for a simple coffee"

Voluntary response bias

Nonresponse bias

Social desirability

Undercoverage

Explanation:

By using the words way too much and simple coffee, the researcher is introducing bias into their question by causing people to favor one response over another.

To avoid this sampling bias, the researcher should use more neutral wording, such as "Agree or diasgree- I would pay \$5 or more for a coffee drink."

### Example Question #3 : How To Identify Sources Of Bias In A Survey

Identify the type of bias:

A researcher wants to know whether students at a particular university have ever cheated on a test. The researcher walks up to 100 random students and asks them the following question:

"Have you ever cheated on a test or exam?"

Undercoverage

Nonresponse bias

Social desirability

Voluntary response bias

Social desirability

Explanation:

Many people are reluctant to be honest about their bad behaviors, especially if they don't believe the survey is confidential. This will cause participants to be more likely to respond with whatever is more socially acceptable.

### Example Question #4 : How To Identify Sources Of Bias In A Survey

The best way to reduce variability in an unbiased sample is to __________.

take a smaller sample

take a random sample of any sort

There is no way to reduce variability in an unbiased sample

take a bigger sample

take a bigger sample

Explanation:

Using random sampling methods alone does not reduce variability in a sample; they only reduce bias. The best way to reduce variability in an unbiased sample is to take a bigger sample—the bigger the population of the sample, the less widespread the results will be. It is important to remember that if there is bias present in a sample, a large sample population size (n value) will not be enough to overcome the bias.

### Example Question #5 : How To Identify Sources Of Bias In A Survey

Identify the type of bias:

A radio station polls listeners on a controversial issue by talking to people who call in to the station.

No bias

Undercoverage bias

Nonresponse bias

Voluntary response bias

Voluntary response bias

Explanation:

Voluntary response bias usually results when those sampled are volunteers who select themselves.
Voluntary response bias can cause results to over represent those who have a strong opinion.

### Example Question #6 : How To Identify Sources Of Bias In A Survey

Identify the type of bias:

A researcher wants to know what proportion of people in the United States favor student debt reform. The researcher goes to five universities and at each asks people whether they favor student debt reform.

No bias

Voluntary response bias

Undercoverage

Nonresponse bias

Undercoverage

Explanation:

This is an example of undercoverage because the researcher did not speak to people who were not affiliated with a university. Therefore the researcher did not adequately sample all members of the overall population (people in the United States).

### Example Question #7 : How To Identify Sources Of Bias In A Survey

You are trying to conduct a survey of students within a college community to see if you should cut funding to the athletics department to save money.  Which of the following manners of conducting this survey would lead to the least bias possible?

Conduct a survey by having an open hotline where students may call in and give their opinion on the matter.

Pull 10 students aside as they walk across campus and ask them to take the survey.

Randomly select a 300 student sample from all of the student body of the school and proctor the survey with those students.

Go to the athletics department and survey 50 student athletes on the issue.

Send out a questionnaire to randomly selected students and look at the ones that are sent back.

Randomly select a 300 student sample from all of the student body of the school and proctor the survey with those students.

Explanation:

The correct answer (random sample of 300 students) includes a random sample which will reduce in bias and also is given to be done in person which reduces completion bias.  It is also taken from the whole population of students and is a large sample which makes it a good representation of the population.  Sending out a questionnaire has completion bias because the only people that will send it back will have strong and possibly biased beliefs already.  The hot line has the same effect as those that have strong and biased opinions will be the ones to do it.  Pulling students aside as they walk by is not a truly randomly constructed sample and using only 10 students is not a good representation of a whole college.  Selecting a sample of just athletes is very biased as they will not want their programs cut.


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Opened 12 years ago

Closed 11 years ago

SVN post commit hook MERGE message reported

Reported by: Owned by: Anders Hedberg Russ Tyndall normal TimingAndEstimationPlugin normal 0.12

Description

When using the latest 0.12 version of the trac-post-commit-hook I got a strange MERGE message back on checkin to subversion. My local copy of the checked in file did not advance the version number, but the subversion repository got the new file-version. The ticket was not updated either.

An older version (I saved previously for 0.11) of the hook script works ok so I assume that it is only the trac-...-hook script that is malfunctioning. I could not find any helpful things in the logs for apache,trac or the hook script itself.

I'm using Eclipse 3.5.2 with Subclipse (which put up the dialogbox with the MERGE message) Subversion on server is version 1.6.12. Trac is 0.12.

comment:1 Changed 12 years ago by Russ Tyndall

Well you haven't given me much to work with here. I have tested that script, but it is modified from my default (which interacts with more/other systems), so their could be bugs. If you message didnt get through that sound like a bug.

Did you get the log for the commit hook or if you did, what was in it? (It looks like by default I have logging setup oddly). But if you are not getting a log make sure that the logfile and LOG variables make sense, and that the script has permission to write to that location. After you get logging of some sort working, please post it here and I will see if we cant get it working.

HTH, Russ

comment:2 follow-up:  3 Changed 12 years ago by Anders Hedberg

This is the log-message of the commit hook on the Trac side. Enjoy ;-)

Begin Log cmd_groups:[(u'references', u'#273 (1)', u'1', u)] cmd:references, tkts#273 (1) tkt_id:273, vals[[<bound method CommitHook?._cmdRefs of <main.CommitHook? inst ance at 0x9c7a74c>>, u'1']] Setting ticket:<trac.ticket.model.Ticket object at 0xa1c1d8c> spent: 1.0

comment:3 in reply to:  2 Changed 12 years ago by Anders Hedberg

This is the log-message of the commit hook on the Trac side. Enjoy ;-)

Begin Log cmd_groups:[(u'references', u'#273 (1)', u'1', u)] cmd:references, tkts#273 (1) tkt_id:273, vals[[<bound method CommitHook?._cmdRefs of <main.CommitHook? inst ance at 0x9c7a74c>>, u'1']] Setting ticket:<trac.ticket.model.Ticket object at 0xa1c1d8c> spent: 1.0

I forgot to add that it looks exactly like the logmessage of the old working script when testing. (besides the 0x-numbers)

comment:4 follow-up:  5 Changed 12 years ago by Russ Tyndall

hrm... well, that looks like it should work (especially if it was matches the old one line for line).

Can I get a copy or screen shot of the weird MERGE message? Also just to make sure I understand:

• The commit to the repository was successful
• Your working copy did not correctly update to the latest new revision
• What is your svn status after the half commit?
• What happens when you svn update?
• I assume this is perfectly repeatable on your end ? (ie: every commit behaves the same)

I am trying to duplicate this on my end at the moment (on a fresh svn repo)

Changed 12 years ago by Anders Hedberg

Attachment: 2010-12-28 21-42-41 Merge error.png added

Merge error

Changed 12 years ago by Anders Hedberg

New try with a gif file and no space...

comment:5 in reply to:  4 Changed 12 years ago by Anders Hedberg

Can I get a copy or screen shot of the weird MERGE message? Also just to make sure I understand:

• The commit to the repository was successful

Yes.

• Your working copy did not correctly update to the latest new revision

Yes.

• What is your svn status after the half commit?

Don't know, not using command line subversion.

• What happens when you svn update?

From the console window in Eclipse (first is commit, then separate update):

commit -m "References #273 (0.5)..." C:/Users/Anders/workspace/Swegon/dummy_test.txt
Sending        Users/Anders/workspace/Swegon/dummy_test.txt
Transmitting file data ...
RA layer request failed
svn: Commit failed (details follow):
svn: MERGE of '/svn/trunk': 200 OK (https://gw.join.ideon.se:447)

G  C:/Users/Anders/workspace/Swegon/dummy_test.txt
Updated to revision 493.
===== File Statistics: =====
Merged: 1

• I assume this is perfectly repeatable on your end ? (ie: every commit behaves the same)

Yes, at least two times. Going into the repository view and then manually overwriting the file from the repository makes the local copy ok.

I am trying to duplicate this on my end at the moment (on a fresh svn repo)

comment:6 Changed 12 years ago by Russ Tyndall

I added some better error logging to the scripts (so you might wish to update like the last 10 lines of your file to match this revision).

You should try running the post commit script manually as below and post any errors you get.

From the trac-post-commit directory try executing:

./trac-post-commit.py -u 'youruser' -p '/var/trac/yourTracUrl' -r 493

I was able to execute mine and get no obvious errors, do you get any?

Thanks, Russ

comment:7 Changed 12 years ago by Russ Tyndall

This is the svn post-commit I am using, it might give you better logging?

#!/bin/bash
log() {
do
echo "[$(date +'%T')]$data" | tee -a $LOG || continue done } set -e REPOS="$1"
REV="$2" CNAME=basename "$REPOS"
export LOGDIR="/var/log/commit-hooks"
LOG="${LOGDIR}/$CNAME.svn-post-commit.log"
mkdir -p "${LOGDIR}" echo "date +'%F' in svn post commit :$REPOS : $REV" | log MESSAGE=svnlook log -r$REV $REPOS AUTHOR=svnlook author -r$REV $REPOS if [ -z "$TRAC_ENV" ] && [ -e "/var/trac/$CNAME" ]; then export TRAC_ENV="/var/trac/$CNAME"
fi

echo "TracEnv:$TRAC_ENV Repo:$REPOS Rev:$REV Auth:$AUTHOR" | log

/usr/bin/python /path/to/your/trac-post-commit.py -p "$TRAC_ENV" -r "$REV" -u "$AUTHOR" -m "$MESSAGE" 2>&1 | log
echo "Done with trac: \$?" | log

comment:8 Changed 11 years ago by anonymous

Resolution: → fixed new → closed

Sorry to bother you with the above. I had an urgent delivery problem and was not able to check more into this at that time, needed to get things out the door to the customer.

I found the error. I had executed the logging post-commit scripts as root on my debian machine for testing, and thus created a log-file owned by root not writeable by the www-data user. When checking in code to svn/apache the scripts was executed as www-data, and there was a "Permission denied" when opening the log/commithook.log file and the trac-post-commit-hook crashed with an IOError exception. (just as it should, just hard to debug this particular error ;-) Thanks for the help with the scripts anyway! /Anders H.

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text:
Solved

# Permission Denied Error on VB Script

Posted on 2009-05-06
486 Views
I receive a permission denied error on line 34, character 10 when I run this script against a folder location that has multiple nested folder levels and lots of files.  I am running the script against the root folder.  I have gone back through and reapplied permissions to every single file and folder for 'Everyone'.  I even made a copy of the entire folder structure, then manually deleted the files and folders using Windows explorer.  This confirmed that there was not a permission issue with accessing the files.  I am running the script locally on the actual computer the folder if located on.  I can run the script against a single folder within the root folder and it works okay.  I can also add each folder into the script text file and it will delete a few then stop with a permission issue.  I assume this has something to do with a filename length or folder name length.

Again, this is not an actual permission issue as I can manually delete all of the files and folders myself.  The script is run locally so it does not have permission issues.
Dim fso, startFolder, OlderThanDate

Dim strFilename, strPath

Set fso = CreateObject("Scripting.FileSystemObject")

strFilename = "c:\work\ee\urgent.txt"

set objFSO = CreateObject("Scripting.FileSystemObject")

if objFSO.FileExists(strFilename) Then

set objFile = objFSO.GetFile(strFilename)

Dim TextStream

Set TextStream = objFile.OpenAsTextStream(1,0)

Dim Line,i

Do While Not TextStream.AtEndOfStream

DeleteOldFiles strPath, OlderThanDate

RemoveEmptyFolders strPath

Loop

Set TextStream = nothing

Else

End If

Msgbox "Old Backup files have been deleted...Done !!"

Function DeleteOldFiles(folderName, BeforeDate)

Dim folder, file, fileCollection, folderCollection, subFolder

Set folder = fso.GetFolder(folderName)

Set fileCollection = folder.Files

For Each file In fileCollection

If file.DateLastModified < BeforeDate Then

fso.DeleteFile(file.Path)

End If

Next

Set folderCollection = folder.SubFolders

For Each subFolder In folderCollection

DeleteOldFiles subFolder.Path, BeforeDate

Next

End Function

'====================

Sub RemoveEmptyFolders(sFolderName)

Dim objFolder, objSubFolders, objFiles

Dim xFolder, xFile

Dim ret

'On Error Resume Next'

Set objFolder = fso.GetFolder(sFolderName)

Set objSubFolders = objFolder.SubFolders

Set objFiles = objFolder.Files

'count files'

iTotFiles=iTotFiles + objFiles.count

For Each xFile In objFiles

xFile.Attributes = xFile.Attributes And Not READONLY

Next

For Each xFolder In objSubFolders

xFolder.Attributes = xFolder.Attributes And Not READONLY

RemoveEmptyFolders (xFolder.Path)

Next

'count directories found'

itotdirs=itotdirs+1

' If the folder is empty then delete the folder.'

If objFiles.Count <= 0 and objSubFolders.count <= 0 Then

iDelDirs=iDelDirs+1

fso.DeleteFolder sFolderName, True

End If

End Sub

0
Question by:murryc
• 2
• 2

LVL 14

Accepted Solution

rejoinder earned 500 total points
ID: 24320774
Can you change line 34 to read;
fso.DeleteFile file.Path
or
fso.DeleteFile file.Path, True

See if either of those help.
0

Author Comment

ID: 24329963
fso.DeleteFile file.Path, True did the trick.

I have another small tweak.  Let me know if you want to me start a new question for it, since you already answered by first question.  This one might be super easy though.

The script deletes files older than a certain number of days.  I need to tweak it to delete files NEWER than 1-1-2009.
0

LVL 14

Assisted Solution

rejoinder earned 500 total points
ID: 24330020
No problem.

You will have to code the date into the variable OlderThanDate;
OlderThanDate = CDate("01/01/2009")
Change this line;
If file.DateLastModified < BeforeDate Then
to this...
If file.DateLastModified > BeforeDate Then

That should do it.
0

Author Comment

ID: 24330805
Worked Perfectly!
0

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text:
# Rectangular Automata

have a question regarding rectangular automata and their derivatives.

In each location the derivates are defined by a interval, how are the derivates applied on the variables? Is one value chosen out of the interval and added to the value or do we reset the value to one value in the interval ?

Regards

• Have you taken a look at the thesis? – Yuval Filmus Jun 19 '18 at 14:45
• I have taken a look at this thesis right now, and i still don't understand how the derivatives work, may i am just not seeing the obvious. – Secr3t Jun 19 '18 at 16:18
• Can you edit the question to provide some background for people who aren't familiar with rectangular automata and their derivatives, summarize what you do understand, and give any references to what you've been reading to learn about this? – D.W. Jun 19 '18 at 21:00
• I am computersience student and i visit a lecture about hybrid systems, in this lecture we are working with hybrid automata, linear hybrid automata, rectangular automata,... A rectangular automata is defined by invariant conditions, guard conditions concerning the edges and derivatives for the different clocks in the automata In the other automatas the derivative for the clocks are all 1. In rectangular automata the derivatives of the clock are definde by an interval, now i am not sure how this works. To we add one value of the interval to the clock in each timeunit ? – Secr3t Jun 19 '18 at 21:30

The derivatives are applied over time in a continuous fashion.

Here is an example:

Assume that we want to find out whom of two runners wins a running tournament. They run for 100 meters each, and the one reaching a goal first wins.

We can model the position of the two runners using two variables $x$ and $y$. We do not quite know the exact speed of the runners, as it depends on how well they feel at the tournament day. But we know some boundaries on their speed, i.e., how $x$ evolves over time. Let's assume we know that $\dot x \in [9.8,9.9] \ \frac{m}{s}$ and that $\dot y \in [9.7,9.78] \ \frac{m}{s}$

So a rectangular hybrid automaton would have one "running" state in which the variables evolve like this, and then there are two states for the cases that runner $x$ has reached the goal and that runner $y$ has reached the goal. You can see from the numbers above that player $x$ will win, but let's assume that this is not obvious, and we want to use a rectangular hybrid automaton for this:

   | x:=0, y:=0
V
+- -------------------+    x >= 100       +---------------------+
| 0.98 <= x' <= 0.99  |------------------>| x' = 0              |
| 0.97 <= y' <= 0.978 |                   | 0.97 <= y' <= 0.978 |
| x < 10, y<10        |                   +---------------------+
+---------------------+
|                       y >= 100       +---------------------+
+------------------------------------->| 0.98 <= x' <= 0.99  |
| y' = 0              |
+---------------------+

If we always "reset the value to one value in the interval", then the two runners would never reach the 100 meter mark and hence one of the two goal states on the right is never right.

But it is also not the case that "one value chosen out of the interval and added to the value". Because adding is a discrete actions. You could, for example, add x' to x until one of the two conditions have been reached. But then, it takes exactly 11 steps for both runners to reach the goal, and hence, they both win at the same time. But that makes no sense, because time is continuous. Rather, if you plot the evolution of x over time, you would use x' as the steepness of the line, and the positions of the runners are really continously updated as time progresses, as in real life.

In rectangular hybrid automata, it doesn't really matter whether $\dot x$ can change at every moment of time to a different value in the interval or not. The reason is that we use these automata for checking the properties of model. In the example above, this would be whether the bottom-right location is ever reached (which is not the case). And for this analysis, whether the first derivatives has to stay constant (within their defined interval) or not does not matter.


text:
99-21   Berichtsreihe des Mathematischen Seminars der Universität Kiel

## Local solvability for positive combinations of generalized sub-Laplacians on the Heisenberg group

As one step in a program to understand local solvability of complex coefficient second order differential operators on the Heisenberg group in a complete way, solvability of operators of the form $\Delta_{S,\al}=\Delta_S +i\al U$, where the leading term $\Delta_S$ is a positive combination of generalized and degenerate generalized sub-Laplacians'', has been studied in a recent article \cite{MPR2} by M. Peloso, F. Ricci and the first named author. It was shown that there exists a discrete set of critical'' values $E\subset \CC$, such that solvability holds for $\al\not\in E$. The case $\al\in E$ remained open, and it is the purpose of this note to close this gap. Our results extend corresponding results in another article \cite{MPR1} by the above mentioned authors, by means of an even simplified approach which should allow for further generalizations.

Mathematics Subject Classification (1991): 22E30, 35A07, 35D05, 43A80

Bibliographical note: erscheint in Proc. Amer. Math. Soc.


text:
qqbarthreshold is hosted by Hepforge, IPPP Durham
 QQbar_threshold
residues.hpp File Reference

Functions to calculate the residues of $$q\bar{q}$$ bound states. More...

Go to the source code of this file.

QQbar_threshold

## Functions

double ttbar_residue (int n, double mu, double m, order o, options opt=top_options())
Computes the residue $$Z_n$$ of an S-wave $$t\bar{t}$$ bound state. More...

complex ttbar_residue (int n, double mu, top_properties M, order o, options opt=top_options())
Computes the residue $$Z_n$$ of an S-wave $$t\bar{t}$$ bound state. More...

double bbbar_residue (int n, double mu, double m, order o, options opt=bottom_options())
Computes the residue $$Z_n$$ of an S-wave $$b\bar{b}$$ bound state. More...

## Detailed Description

Functions to calculate the residues of $$q\bar{q}$$ bound states.

Version
2.2.0


text:
# Revision history [back]

Quick proposition:

sage: L = [1, 3, 2]
sage: sum([b*x^a for a,b in list(enumerate(reversed(L)))])
x^2 + 3*x + 2

Quick I am not sure that Sage shoud contain a function for each such feature, it will lead to a huge namespace, making tab completion unusable. Here is a quick proposition:

sage: L = [1, 3, 2]
sage: sum([b*x^a for a,b in list(enumerate(reversed(L)))])
enumerate(reversed(L))])
x^2 + 3*x + 2

I am not sure that Sage shoud contain a function for each such feature, it will lead to a huge global namespace, making tab completion unusable. Here is a quick proposition:

sage: L = [1, 3, 2]
sage: sum([b*x^a for a,b in enumerate(reversed(L))])
x^2 + 3*x + 2

Or, if you want a function, define:

sage: poly2sym = lambda L : sum([b*x^a for a,b in enumerate(reversed(L))])
sage: poly2sym([1, 3, 2])
x^2 + 3*x + 2

Now, if you want genuine polynomials (not symbolic functions), you can define the polynomial ring you want and build a polynomial from a list as follows:

sage: R.<x> = PolynomialRing(QQ)
sage: R
Univariate Polynomial Ring in x over Rational Field

sage: R([1, 3, 2])
2*x^2 + 3*x + 1

As you can see, the order is not the one you wanted, so you can do:

sage: R(list(reversed([1, 3, 2])))
x^2 + 3*x + 2

And again:

poly2sym = lambda L : R(list(reversed(L)))

But then, you should understand that the prouced object are genuine polynomials, not symbolic expressions as before.


text:
# A car of mass $750\;kg$ moves around a circular track of radius $50\;m$ with a speed of $10\;ms^{-1}$. What's the centripetal force on the car?
$\begin{array}{1 1} 21.7\;N \\ 1500\;N \\ 2.79\;N \\3.64\;N \end{array}$


text:
### Abstract:

Operators AA and BB don't commute precisely when their commutator AB−BAAB−BA is nonzero. From quantum mechanics, we know that noncommuting operators are a fact of life and the question of which operators can arise as single commutators in various settings is of interest, {\it e.g.,} the Heisenberg commutation relations. We will describe some

classical results and some more recent results, as well as open problems and conjectures, about single commutators, sums of commutators and related topics.

Speaker

Ken Dykema

Research Area
Affiliation

Texas A & M University

Date

Fri, 14/10/2016 - 2:00pm to 3:00pm

Venue

RC-4082, The Red Centre, UNSW


text:
# Finding the value of a constant in a joint probability density function

Given a joint density function $f(x, y) =Ae^{-x-y}$, where $0 < x < y < \infty$, find the value of the constant $A$.

To find the value of $A$, clearly I need to take the double integral, however I'm struggling to work out what the limits should be. What should they be?

## 2 Answers

$\int_{0}^{\infty}\int_{x}^{\infty} {Ae^{-x-y}}dydx=\int_{0}^{\infty}Ae^{-x}\int_{x}^{\infty}e^{-y}dydx=\int_{0}^{\infty}Ae^{-2x}dx={A\over2}=1\to A=2$

We have the following situation as equivalent to $$\int_{0}^{\infty} \int_{0}^{y} Ae^{-x}e^{-y}\, dx \, dy = 1$$ $$\int_{0}^{\infty} Ae^{-y}\left (1-e^{-y}\right)\, dy =1$$ $$\implies A - \frac {A}{2} =1$$ $$\implies A=2$$


text:
Skip to main content
$$\require{cancel}$$

# 1.1: Introduction

This is the first in a series of chapters on electricity and magnetism. Much of it will be aimed at an introductory level suitable for first or second year students, or perhaps some parts may also be useful at high school level. Occasionally, as I feel inclined, I shall go a little bit further than an introductory level, though the text will not be enough for anyone pursuing electricity and magnetism in a third or fourth year honours class. On the other hand, students embarking on such advanced classes will be well advised to know and understand the contents of these more elementary notes before they begin.

The subject of electromagnetism is an amalgamation of what were originally studies of three apparently entirely unrelated phenomena, namely electrostatic phenomena of the type demonstrated with pieces of amber, pith balls, and ancient devices such as Leyden jars and Wimshurst machines; magnetism, and the phenomena associated with lodestones, compass needles and Earth’s magnetic field; and current electricity – the sort of electricity generated by chemical cells such as Daniel and Leclanché cells. These must have seemed at one time to be entirely different phenomena. It wasn’t until 1820 that Oersted discovered (during the course of a university lecture, so the story goes) that an electric current is surrounded by a magnetic field, which could deflect a compass needle. The several phenomena relating the apparently separate phenomena were discovered during the nineteenth century by scientists whose names are immortalized in many of the units used in electromagnetism – Ampère, Ohm, Henry, and, especially, Faraday. The basic phenomena and the connections between the three disciplines were ultimately described by Maxwell towards the end of the nineteenth century in four famous equations. This is not a history book, and I am not qualified to write one, but I strongly commend to anyone interested in the history of physics to learn about the history of the growth of our understanding of electromagnetic phenomena, from Gilbert’s description of terrestrial magnetism in the reign of Queen Elizabeth I, through Oersted’s discovery mentioned above, up to the culmination of Maxwell’s equations.

This set of notes will be concerned primarily with a description of electricity and magnetism as natural phenomena, and it will be treated from the point of view of a “pure” scientist. It will not deal with the countless electrical devices that we use in our everyday life – how they work, how they are designed and how they are constructed. These matters are for electrical and electronics engineers. So, you might ask, if your primary interest in electricity is to understand how machines, instruments and electrical equipment work, is there any point in studying electricity from the very “academic” and abstract approach that will be used in these notes, completely divorced as they appear to be from the world of practical reality? The answer is that electrical engineers more than anybody must understand the basic scientific principles before they even begin to apply them to the design of practical appliances. So – do not even think of electrical engineering until you have a thorough understanding of the basic scientific principles of the subject.

This chapter deals with the basic phenomena, definitions and equations concerning electric fields.


text:
# Coloring graph with maximum vertex degree $< k$ so every vertex is a starting point for a path containing each color

Given an undirected graph ($V$ vertices, $E$ edges) with maximum vertex degree $< k$ I want to find a vertex coloring using exactly $k$ colors so that no two adjacent vertices have the same color and for each vertex there exists a path starting in it such that no two vertices on this path has the same color and it contains exactly $k$ vertices. Additionaly, I know that in this graph there is at least one cycle of length exactly $k$. Have you got any ideas how to tackle this problem?

• The paths you are talking about actually have nothing to do with Hamiltonian paths, right? Better edit the title and the tags. – Mikhail Tikhomirov Sep 28 '17 at 9:37
• Dear @Userbejian29: please note that your use of "bounded degree" is sort-of-a-misuse of standard graph-theoretic terminology: 'bounded degree' is used if the context contains an infinite sequence of graphs. (Search for yourself.) What you mean is simple 'with maximum degree $<k$'. This is a usual way to put it. Would you please say it this way? (Unless for some strange reason you really really insist on this unusual use of 'bounded degree'.) – Peter Heinig Sep 28 '17 at 10:17

The OP is asking for something which has already been proved to exist in

Saieed Akbari, Vahid Liaghat, Afshin Nikzad: Colorful Paths in Vertex Coloring of Graphs, The electronic journal of combinatorics 18 (2011), #P17

(see Theorem 3 on page 5 of op. cit., which is exactly what the opening post is asking for, except for a necessary exclusion of $G\cong C^7$.)

• @MikhailTikhomirov: thanks for pointing out. This is not my intent. I find the 'reference request' section, within reason, very valuable. I will edit the answer. But an answer it is, I think. (Though it should be Theorem 3, not 1). I will edit. – Peter Heinig Sep 28 '17 at 10:41


text:
# Lstlisting Python

I'm usinglistingspackage to put a python code inside an article. I want it to be written in \ttfamily. The problem is I can't change keywordstyle to bold text.

\documentclass{article}
\usepackage{listings}

\lstset{basicstyle=\ttfamily, keywordstyle=\bfseries}

\begin{document}
\begin{lstlisting}[language=Python]
if x==0:
print(x)
\end{lstlisting}
\end{document}

Any help please ? Thanks !

You need a font that has a bold version of the typewriter family. If you look in the .log file you will find:

LaTeX Font Info:    Font shape OT1/cmtt/bx/n' in size <10> not available
(Font)              Font shape OT1/cmtt/m/n' tried instead on input line 9.

A recent new choice of typewriter font with a bold version is provided by the newtxttt package:

\documentclass{article}

\usepackage{listings,newtxtt}

\lstset{basicstyle=\ttfamily, keywordstyle=\bfseries}

\begin{document}
\begin{lstlisting}[language=Python]
if x==0:
print(x)
\end{lstlisting}
\end{document}

An alternative is the zlmtt package:

which fits better with the standard computer modern fonts of LaTeX.

If you do not wish to change fonts in this way and just want to use the ordinary bold font, then you should switch to \rmfamily before selecting \bfseries:

\documentclass{article}

\usepackage{listings}

\lstset{basicstyle=\ttfamily, keywordstyle=\rmfamily\bfseries}

\begin{document}
\begin{lstlisting}[language=Python]
if x==0:
print(x)
\end{lstlisting}
\end{document}

You can use lmodern with the lighttt option.

\documentclass{article}
\usepackage[lighttt]{lmodern}
\usepackage{listings}

\lstset{basicstyle=\ttfamily, keywordstyle=\bfseries}

\begin{document}

\begin{lstlisting}[language=Python]
if x==0:
print(x)
\end{lstlisting}

\end{document}

Without the lighttt option:

Latin Modern fonts are mostly equivalent to Computer Modern. However, the boldface version of Latin Modern Mono is not so distinct from the medium font, so the lighttt option uses a light series instead of medium.

You can also use any other mono font, maybe scaling it to fit the text font, for instance FiraMono:

\documentclass{article}

\usepackage[scaled=0.85]{FiraMono}
\usepackage{listings}

\lstset{basicstyle=\ttfamily, keywordstyle=\bfseries}

\begin{document}

Abc\texttt{Abc}

\begin{lstlisting}[language=Python]
if x==0:
print(x)
\end{lstlisting}

\end{document}


text:
Volume 282 - 38th International Conference on High Energy Physics (ICHEP2016) - Astro-particle Physics and Cosmology
Type II leptogenesis
L. Covi, J.E. Kim,* B. Kyae, S. Nam
*corresponding author
Full text: pdf
Pre-published on: 2017 February 06
Published on: 2017 April 19
Abstract
We discuss our new theory on baryogenesis Type-II leptogenesis' \cite{CoviKim16} which is different from the well-known Type-I leptogenesis' \cite{FY86}. First, we will briefly comment on the Jarlskog phases in the CKM and PMNS matrices, $\delta_{CKM}$ and $\delta_{PMNS}$. Then, the PMNS phase is used in the `Type-II' leptogenesis for Sakharov's condition on the global quantum number generation in the Universe. For this to be effective, the SU(2)$\times$U(1) gauge symmetry must be broken during the leptogenesis epoch.
Open Access