Perturbation Definition and 378 Threads

I'm rather stuck on this problem. I seem to be having issues with the simplest things on this when trying to get started. Homework Statement There is a particle with spin-1/2 and the Hamiltonian H_0 = \omega_0 S_z. The system is perturbed by: H_1 = \omega_1 S_x e^{\frac{-t}{\tau}}...

I need some example driven learning material for my "singular perturbation" class. Someone help me please.

As expected, my textbook and teacher are both lacking clear, concise examples for me to work with, so would someone point me to early examples within the context of "perturbation techniques", preferably with WORKED OUT solutions for cross reference? thanks

Ok so I have a classic particle in a box problem. If a particle in a box, the states of which are given by: ψ = (√2/L) * sin(nπx/L) where n=1,2,3... is perturbed by a potential v(x) = γx , how do I calculate the energy shift of the ground state in first order perturbation I'm guessing that...

I want to know about relativistic correction to perturbation. I searched but failed to find any teaching on this topic. Is it true that we just need to replace the non-relativistic Hamiltonian perturbation terms with the relativistic ones while leaving the perturbation formulae unchanged...

It is easy to understand for example how Jupiter pulls (perturbation) the orbit of the Earth more elliptic. But after a certain period the orbit will again be more circular. How does that (the opposite) work ?

the spin orbit coupling removes the degeneracy but not completely, should we still use the degenerate perturbation theory. is it because of relativistic corrections? Thanks!

The following comes from Landau's Statistical Physics, chapter 32. Using a Hamiltonian \hat{H} = \hat{H}_0 + \hat{V} we get the following expression for the energy levels of a perturbed system, up to second order: E_n = E_0^{(0)} + V_{nn} + \sideset{}{'}{\sum}_m \frac{\lvert...

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...

i see people discussing the convergence radius of a perturbation series in the literature i am really baffled generally, one can only get the first few coefficients of a perturbation series that is, the perturbation series is not known at all how can one determine the convergence...

Homework Statement I'm looking at the 1d harmonic oscillator \begin{equation} V(x)=\frac{1}{2}kx^2 \end{equation} with eigenstates n and the time dependent perturbation \begin{equation} H'(t)=qx^3\frac{(\tau^2}{t^2+\tau^2} \end{equation} For t=-∞ the oscillator is in the groundstate...

The singularity theorems apply to situations away from exact symmetry ... away from Schwarzschild solution or Friedmann solutions for example. There are a number of accounts of the singularity theorems but none addressing the problem of proving a 'trapped set' still persists after slight...

The problem given is a perturbation on the two dimensional harmonic oscillator where the perturbation is simply: H'=-qfy. It seems that all of the elements of the matrix H' are zero and so constructing a diagonal matrix in the subspace is eluding me. Any ideas?

Hello guys. I was told to prepare a presentation on perturbed Einstein's field equation by my advisor. I got some of the things I needed to start with in the Weinberg's Cosmology book but it was not enough. Can anyone please tell me a book or anything with information on metric perturbation? Thanks

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 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...

Homework Statement The potential of a simple harmonic oscillator of HF has the following form \frac{1}{2}kx^2 + bx^3 + cx^4 The first part of the problem involved finding expressions for the first-order energy corrections for the first three states, which I found below. Basically the x3 term...

Hello! I am answering a problem which involves spins in the hamiltonian. The hamiltonian is given by H = B(a1Sz^(1) + a2Sz^(2)) + λS^(1)dotS^(2). The Sz^(1) and Sz^(2) refers to the Sz of the 1st and 2nd spins respectively. B is the magnetic field and the others are just constants. The...

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...

Homework Statement "A ball is tossed upwards with speed V_0. Air resistance is -mkv^2 and there's gravity too. Find the the time it takes the ball to reach the maximum height. Do not solve the equation of motion exactly. Use the perturbation method on the equation of motion. Solve the equation...

Hi, Is there any way to analytically calculate the perturbation of a uniform electrostatic field by a dielectric cube. I know a solution exists for dielectric spheres but I haven't been able to come across the solution, when dealing with a cube. Ohh.. and I'm assuming the simplest case...

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...

Homotopy Analysis Method (or Homotopy Perturbation Method)?? How effective is this Homotopy Analysis Method (HAM) in solving coupled non-linear PDE? I see some papers, but they seem to be cross-referencing a small group of people most of the time. This sounds strange for a method that is so...

Homework Statement Let's consider a harmonic oscillator with a harmonic perturbation: H = \frac{p^2}{2} + \frac{x^2}{2} + a \frac{x^2}{2}. Exact solution is known, but we want to derive it using perturbation theory. More specifically, suppose we want to obtain a series for the ground state...

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...

Perturbation-the ability of an unperturb system to remain the same when a perturb system is added to it. Can't really understand this?

Pls. answer in the simplest and the most intuitive way. 1. What is the reason our quantum field theory needs perturbative approach. Is it because in the concept of fields, there is an infinite number of freedom in the oscillations of the virtual particles, or is it because the field is...

Pleae help me. a),b),c) was already solved. but question d) is not.

Homework Statement \epsilon\frac{d^{2}u}{dx^{2}} +\frac{du}{dx} + e-x = 0 0<x<1 u(0)=0 u(1)=1 Homework Equations The Attempt at a Solution i want to find the inner solution first i used the substitution x=\epsilon2y i put that in the equation...

We can apply perturbation to Helium. ıt has two electrons. But Mercury has lots of electrons. in this case, can we apply perturbation to Mercury? How?

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...

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}>...

let be m a measures (by expermients) physical quantity and m0 a 'bare' value of these physical quantity , let us suppose that we can expand m= m_{0}+f(k,m_{0})+ \sum_{n} u^{n}c_{n} for some finite quantities c_n and u=log(\Lambda) with lambda a regulator can we then invert the...

Please teach me this: Can we demontrate the convergence of perturbation series of quantum field theory(Feymann diagrams) after making the renormalizing procedure? If we can't demontrate that,why we still consider the perturbative method using in quantum field theory being useful and believable...

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.

Homework Statement consider a perturbation to the simple harmonic oscillator problem Lambda* (x)^4 question a) show tht the first order correction to n-th eigenstate is proportional to (1+2n+2n^2) b) argue that no matter how small lambda is ,the perturbation expansion will break down for...

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...

Homework Statement During my calculation of hydrogen atom perturbation, I need to integral below in cartesian coordinate. It is given that below integral can be transformed. Homework Equations Anyone could help to see what will the transformed integral in polar coordinate if the...

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...