Perturbation theory Definition and 237 Threads

Take the usual time-independent perturbation theory in QM for example,H'=H_0+V, a basic assumption is we can expand the new states of H' in terms of the old ones of H_0, most of the textbooks justify this assumption by reasoning that the set of eigenfunctions of Hamiltonian is complete...

Homework Statement Going over and over the perturbation theory in various textbooks, I feel that I've NEARLY cracked it. However, in following a particular derivation I fail to understand a particular step. Could anyone enlighten me on the following? Multiply |\psi^{1)_{n}>...

Hi all. Just have a quick question on perturbation theory. Let's consider a molecule in ground electronic state. If a time-independent external perturbation acts on the molecule, the average electronic energy is going to change. From time-independent perturbation theory, we know that <E> =...

Hi I was wondering if someone could help me out. I have been studying TDPT and was wondering how it applies to atomic physics or if someone could give me a example that would be great.

I need to find the roots of the transcendental function, f(x;a)=x^2-3ax-1-a+exp(-x/a)=0; I've done many problems like this before and am fairly sure this is just a regular perturbation problem. The difficulty I'm having is with the exponential term. Could anyone give me an idea of how...

Homework Statement A Hydrogen atom is initially in its ground state and then subject to a pulsed electric field E(t)=E_{0}\delta(t) along the z direction. We neglect all fine-structure and hyperfine-structure corrections. Homework Equations 1. It is important to use selection rules to avoid...

Homework Statement Use leading order perturbation theory to calculate the ground state shift of hydrogen due to perturbation: \hat{V} Homework Equations 1. Leading terms in expansion of energy: E=mc^{2}+\frac{p^{2}}{2m}-\frac{p^{4}}{8m^{3}c^{2}}+... 2. \hat{H}=\hat{H}_{0}+\hat{V} where...

I've been working my way through some basic quantum mechanics, and have gotten up to perturbation theory. It basically makes sense to me, but there's one thing that bothers me, and I was wondering if somebody could shed some light on it. The essential idea behind perturbation theory is that we...

We all know from time-independent perturbation theory that if we have an atom in ground state [0>, and when a time-independent perturbation acts on it, the energy of the ground state gets shifted and the ground state wave function also gets modified. Using Time-independent Schroedinger eq...

Homework Statement Consider the first excited state of the Hydrogen atom. The principle quantum number is given by n = 2 and so it is four-fold degenerate. Consider now a weak perturbation in the form of V = λxy, where x and y are the Cartesian coordinates of the electron with respect to the...

I have been using time-dependent perturbation theory for quite a while. Yet, one thing is still not clear to me. I have seen in many books and papers that when they calculate the transition amplitudes, they integrate from 0 to t. While in many other papers and books, the limit is taken to be -...

Homework Statement A particle of mass m is in the ground state in the harmonic oscillator potential V(x) = \frac{1}{2}Kx^{2} A small perturbation \beta x^{6} is added to this potential. How small must \beta be in order for perturbation theory to be valid? Homework Equations...

Does anyone kown how to apply time dependent perturbation theory to densities matricies (I'm interested in first order)? Thanks.

In my quest to learn quantum mechanics I've become a little confused and I have a question. It is "In The Feynman Lectures on Physics Volume 3, is most of the work, eg. ammonia molecule done using perturbation theory or is this method something else, not perturbation theory?" I started to...

Hi I was just reading about that total derivatives in the Lagrangian does not give any contributions in perturbation theory but that they can play role in non perturbative regimes. But there was no statement WHY that is so? Does anyone have an idea and reading advices? I have the most...

Hello, I was wondering whether anyone knows the Feynman rules for Chiral Perturbation theory? I am trying to calculate K->PiPi and have obtained the relevant diagrams but cannot proceed without the relevant feynman rules.

Perturbation Theory Help! Hello physicsforums.com, The last two weeks of my nuclear engineering course covered a mathematical topic known as 'perturbation theory'. It was offered as a 'method to solve anything' with; the problem is, however, that nobody in my class understands it. Basic...

Homework Statement An electron is confined by the potential of a linear harmonic oscillator V(x)=1/2kx2 and subjected to a constant electric field E, parallel to the x-axis. a) Determine the variation in the electron’s energy levels caused by the electric field E. b) Show that the second order...

Hi I'm referring to the book Quarks and Leptons (Halzen, Martin). On pages 79-82 nonrelativistic perturbation theory is investigated (i.e. by using the Schroedinger equation, which is first order in time). On Page 85, however, the transition amplitude (T_fi) is used that has been derived on...

Homework Statement I am looking at the relativistic correction to the kinetic energy for a hydrogen atom. I am told that the perturbation is usually written as H = -p^4/(8 m^3 c^2) and need to find the energy shift Homework Equations I know that from the perturbation theory the energy...

Does anybody happen to know where to find the perturbation theory formulas for the energies and states up to fourth order? I have to do a calculation up to this order and don't want to have to derive them if I don't have to (I know that Wikipedia has high order energies, but they only have the...

Homework Statement A hydrogen atom is placed in a uniform electric field E(t) given by E(t) = Enaught*exp(-a*t) (where a is a constant) for t >0. The atom is initially in the ground state. What is the probability that, as t→∞ , the atom makes a transition to the 2p state? I know...

Hi everyone, I'm trying to work on Problem 5.32 from Sakurai's Modern Quantum Mechanics. In a nutshell, we need to use Perturbation Theory to find some of the energy levels of Positronium. Here's the full problem: http://img714.imageshack.us/img714/6515/sakurai532.gif Problem 3.3 isn't much...

Homework Statement The length of a pendulum is slowly doubled (l=l_0(1+epsilon*t), 0<=t<=1/epsilon). How does the amplitude q_max of the oscillations vary? Any hints? Homework Equations The Attempt at a Solution

Homework Statement Hi, i have put the question, my attempt and actual answer in the attached picture. My answer is not quite right; firstly why is the second term a minus lambda, and where does the O(lamdba^2) come from? Homework Equations The Attempt at a Solution

Hi, I am basically trying to put a wavefunction into the Time Dependant Schrodinger Eqn, as shown in my lecture notes, but i don't understand one of the steps taken... |\right \Psi (t)\rangle=\sum c_n (t) |\right u_n\rangle e^-(\frac{E_n t}{\hbar}) into i\hbar \frac{\delta}{\delta t}|\right...

The potential of an electron in the field of a nucleus is: -Ze^2/(4 Pi Epsilon0 r) r > r0 -Ze^2/(4 Pi Epsilon0 r0) r <= r0 where r0 is the fixed radius of the nucleus. What is the pertubation on the normal hydrogenic Hamiltonian? Calculate the change in energy of the 1s state to the first...

Homework Statement 1. A particle of mass M is in a square well, subject to the potential: V(x)= V0\theta(x-a/2) for x in (0,a) and diverges elsewhere, where theta is heaviside step function. In perturbation theory, find O(V0^2) correction to the energy and O(V0)to the eigenstate. 2. A...

Homework Statement Regard the nucleus of charge Ze as a sphere of radius R0 with uniform density. Assume that R0<<a0 where a0 is Boher radius/ 1. Derive an expression for the electrostatic potential V(r) between the nucleus and the electrons in the atom. If V0(r)=-Ze^2/r is the potential...

Hi all Please look at this link (Search for the phrase "The quantum state at each instant can be expressed as a linear combination of the eigenbasis"): http://en.wikipedia.org/wiki/Perturbation_theory_%28quantum_mechanics%29 If we write the wavefunction for the perturbed system as a...

Homework Statement Consider a quantum particle of mass m in a 3-D harnonic potential with frequency \omega and it experiences a perturbation H_{1}=az^{2} a. Determine the effect of H_{1} on the 1st exicted level of the system ( at the 1st order perturbation) b. what happen to L^{2} and...

a particle moves in one dimension in the potential V(x)=\infty \forall |x|>a, V(x)=V_0 \cos{\frac{\pi x}{2a}} \forall |x| \leq a now the unperturbed state that i use is just a standard infinite square well. anyway the solution says that perturbation theory is only valid provided that...

Hi together... When reading Sakurai's Modern Quantum Mechanics i found two problems in the chapter "Approximation Methods" in section "Time-Independent Perturbation Theory: Nondegenerate Case" First: The unperturbed Schrödinger equation reads H_0 | n^{(0)}\rangle=E_n^{(0)}...

Consider a system of a rigid rotator together with a uniform E-field directing along z-axis. So to calculate the perturbed energy and wavefunction we have to use perturbation theory. But the book said we can use non-degenerate one to calculate the result. I wonder why. It is because the original...

Dear All, I have recently read about WKB approximation and about perturbation theory. Both methods are applicable in the range of slowly varying potentials. What I have not understood is which is the range of applicability of one of the method compared with the other one. More...

Homework Statement Hi I am trying to apply degenerate perturbation theory to a three dimensional square well v= 0 for x, y,z interval 0 to a, perturbed by H' = xyz (product) from 0 to a, otherwise infinite. I need to find the correction to energy of the first excited state which I know is...

Homework Statement Why can't we use perturbation theory to calculate the effect of the spin orbit interaction in hydrogen like uranium? Homework Equations The Attempt at a Solution Is it something to do with the fact that the perturbation must be small compared to the rest of the...

Homework Statement A particle of charge q and mass m is in a harmonic oscillator potential V0=0.5m(wx)^2. A perturbation is introduced which changes the potential to V=V0 + dV with dV=0.5sm(wx)^2 where s is small. Use perturbation theory to compute the first order shift in the ground state...

Hi all. I'm reading about time-independent perturbation theory for degenerate states in Griffiths' Introduction to QM. I have a question on the things he writes in chapter 6.2, page 269. What does he mean by the so-called "good" linear combinations? I hope you can shed some light on...

why in time independent degenerate perturbation we diagonalize the matrix of the perturbation part of the hamilitonian and not the original hamiltonian?

Homework Statement Given the Hamiltonian and perturbation below, what are the energy shifts for the states with l=1 Given H_{0}=(L^2)/(2I) H_{1}=E_{1}cos\vartheta Homework Equations L= r x P The Attempt at a Solution in order to find the first order correction to the energy...

I'm trying to follow some working by lecturer; Treating delK (previously found in first bit of question), show that the energy En of the usual hydrogenic state [nlm> is shifted by some expression given. basically we start with \[ \frac{1}{2m_{0}c^{2}} \left\langle...

Homework Statement Question: If a particle is in the ground state at time t<0, use the 1st order time dependent perturbation theory to calculate the probability that the particle will still be in the ground state at time t. Suppose we turn on the perturbation at time t=0 H(x) = ax...

Homework Statement A Hydrogen atom in its ground state (n,l,m) = (1,0,0) is placed in a weak electric fieldE(t) = 0 if t < 0 Eo *e^{\frac{-t}{\tau}} if t > 0E is in the positive z direction What is the probability that it will be found in any of the n=2 states at time t > 0 ? use...

I have been told before that virtual particles are just an artefact of perturbation theory, that if we could solve interacting fields exactly we would have no need to talk about virtual particles at all. My question then is if virtual particles are just a mathematical tool to evaluate...

I have an infinite potential well with length L. The first task was to calculate the eigenvalues and -functions for the energy of a particle in the well. The requirements were \psi(0, L) = 0 and there is no time-dependence. I've calculated: \hat{H}\psi(x) = E\psi(x) E =...

Hello, I have to learn about the classic Perturbation Theory. I'm looking for guides, textbooks etc about Perturbation Theory. I already know the basis (Poincare method), but I found it hard to find resources for more advanced material on the one hand, that will also teach it from basis on...

First of all, I'm sorry about the last topic, accidentally I switched between the previous message and this one... Sorry about the troubles. I think it's the right forum (after reading a bit), sorry if I'm wrong... My high school graduation project is about the perturbation theory, it's...

Homework Statement The Hamiltonian for a rigid diatomic molecule is H_0 = {L^2 \over {2I}} where I is the moment of inertia of the molecule. (a) What are the lowest four energy states of this system? (b) An external electric field is applied, leading to a perturbation H_1 = ED\cos\theta...

From the following attachments I understand how the roots of the equation and the perturbation coefficients were found. What I don't get is the solid line in the graph that is allegedly the plot of two of the three roots versus epsilon. Can somebody clear this up for me? Also, how would I...