Perturbation theory Definition and 267 Threads

Hi all, I have a question about perturbation theory and the fine structure constant. Consider an electron moving through the vacuum - this wil induce vacuum polarization, and (if I understand correctly) perturbation theory can be used to analyze the situation. My question is essentially: if...

hey, say you have a infinite potential well of length L, in the middle of the well a potential step of potential V and length x. Inside the well is a particle of mass m. why are the first order energy corrections large for even eigenstates compared to odd ones? also, say well...

time-independent, non-degenerate. I am referring to the following text, which I am reading: http://www.pa.msu.edu/~mmoore/TIPT.pdf On page 4, it represents the results of the 2nd order terms. In Eqs. (32), (33) and (34) I don't understand the second equality, i.e. basing on which formula he has...

Hi I am reading about Degenerate Perburbation Theory, and I have come across a question. We all know that the good quantum numbers in DPT are basically the eigenstates of the conserved quantity under the perburbation. As Griffiths he says in his book: "... look around for some hermitian...

Many of you stated how ad hoc is QFT as the field is supposed to be non-interacting yet how could they get an incredibly accurate value of calculated magnetic moment of the electron of value 1.0011596522 compared to measured 1.00115965219 with accuracy to better than one part in 10^10, or...

Hi all ! I need some help Homework Statement The nucleus of an hydrogen-like atom is usually treated as a point charge Ze. Using the first order perturbation theory, estimate the error due to this approximation assuming that the nucleus is a sphere of radius R with a uniform charge...

Hi all, I have a tricky problem in pertubation theory. I have a function: f(\vec{r}) = P(\vec{r}) + \left( B(\vec{r}) + b(\vec{r}) \right)^2 where b(\vec{r}) is a small perturbation and is equal to 0 when P(\vec{r}) = 0 Now, to solve the equation \nabla f(\vec{r}) = 0 for b(r) is...

Hi all. I have been thinking about a very simple question, and I am a little confused. We know from time-independent perturbation theory that if the system is perturbed by the external perturbation λV which is much smaller compared to the unperturbed hamiltonian H0, we can write the ground state...

Hey everyone, I'm studying quantum mechanics from Griffiths (Introduction to Quantum Mechanics, 2nd edition), and I'm puzzling over his derivation of the nth order corrections to the energies and corresponding eigenstates for a perturbed Hamiltonian. The steps that are outlined in Griffiths...

Homework Statement Consider the following Hamiltonian. H=\begin{pmatrix} 20 & 1 & 0 \\1 & 20 & 2 \\0 & 2 & 30 \end{pmatrix} Diagonalize this matrix using perturbation theory. Obtain eigenvectors (to first order) and eigenvalues (to second order). Ho=\begin{pmatrix} 20 & 0 & 0 \\0 & 20 & 0...

I'm studying a perturbation theory (behaviour of its series) and have found two articles which might be of particular interest. Unfortunately, all my three institutions do not have subscription to these journals (articles are too old). I'm kindly asking for your help. These are the articles I'm...

Hi, If we have a non degenerate solution to a Hamiltonian and we perturb it with a perturbation V, we get the new solution by |\psi_{n}^{(1)}> = \sum \frac{<\psi_{m}^{(0)}|V|\psi_{n}^{(0)}>}{E_n^{(0)} - E_m^{(0)}}\psi_m^{(0)} where we sum over all m such that m\neq n. When we do the same...

I'm studying Sakurai at the moment, time-dependent perturbation theory (TDPT). I'm having a problem in understanding a basic concept here. According to Sakurai we have the following problem: Let a system be described initially by a known hamiltonian H0, being in one of its eigenstates |i>...

Time-dependant perturbation theory & "transitions" I'm studying approximation methods, and something is really bothering me about the standard treatment of time-dependant perturbation theory. In lecture, the prof introduced time-dependant perturbation theory with the following motivation...

Why when we analyse time dependant perturbation theory, we take that the diagonal elements of matrix <i|W(t)|j> are equal to zero? Why in degenerate perturbation theory we assume that perturbed wavefunctions of degenerate states can be expressed in the base of unperturbed wavefunctions of...

So in time-independent degenerate perturbation theory we say that we can construct a set of wavefunctions that diagonalize the perturbation Hamiltonian (H') from the degenerate subspaces of the unperturbed Hamiltonian (Ho). Since the original eigenstates are degenerate, combinations of them are...

Homework Statement Question is: Prove the following: Let A be a Hermitian operator that commutes with H0 and perturbation H'. If two degenerate states have distinct eigenvalues for A, then the matrix element of perturbation between them is zero! The real problem is I don't understand...

My question pertains to the following article: http://tinyurl.com/4uw9h2a I have attached the relevant section to this post. My question is whether Godin's assertion is correct or not - namely the sentence "Such a development ... additional terms" and the last sentence in the attachment...

Homework Statement I'm trying to derive the second-order correction of energy in time independent perturbation theory. My professor did it the Landau's way so I'd rather use his notation (without bra and kets). I already derived the first-order correction: E_n^{(1)}=V_{nn}=\int...

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...

A particle is in the ground state in a one-dimensional box given by the potential v(x)= 0 for 0<x<a v(x)= inifinity other wise A small perturbation V = V(0)x/a is now introduced. Show, correct to first order in perturbation theory, hat the energy change in the ground state is V(0)/2...

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...