Perturbation Definition and 426 Threads

Please help me try to understand this problem. It deals with the quantum-confined Stark effect in nanoparticles. For odd n, n = 1, 3, 5, ... \psi_{n}(x) = \sqrt{\frac{2}{a}} \cos (\frac{n \pi x}{a}) and for even n = 2, 4, 6, ... \psi_{n}(x) = \sqrt{\frac{2}{a}} \sin (\frac{n \pi x}{a}) and...

Homework Statement I'm given that a harmonic oscillator is in a uniform gravitational field so that the potential energy is given by: V(x)=\frac{1}{2}m\omega^2x^2 - mgx, where the second term can be treated as a perturbation. I need to show that the first order correction to the energy of a...

Homework Statement Consider a perturbed hydrogen atom whose Hamiltonian, in atomic units, is: H= -1/2(∆^2) – ½ + b/(r^2) (∆ should be upside down), where b is a positive constant. The Schrodinger equ. for this hamiltonian can be solved exactly for the energy eigenvalues. The...

Time dependent perturbation theory... second order term... For some reason they replace <E_{n}|H_{0}^2|E_{m}> with \Sigma<E_{n}|H_{0}|E_{i}><E_{i}|H_{0}|E_{m}> I know why they are allowed to do this, what I don't understand is how it makes my life better?

Hi, I'm working out the 2nd Edition of Quantum Mechanics by Bransden & Joachain and I'm a little puzzled by the sign of the last term in equation 8.30 on page 380, which reads... a_{nl}^{(2)} = \frac{1}{E_n^{(0)} - E_l^{(0)}}\sum_{k{\neq}n} \frac{H_{lk}^{'}H_{kn}^{'}}{E_n^{(0)} - E_l^{(0)}}...

I know what Bifurcation Theory is. but What is Perturbation theory? is it similar to bifurcation theory?

-Ok..Let,s be the Hamiltonian H=H_0 +W in one dimension where W is a "weak" term so we can apply perturbation theory. -The "problem" comes when we need to calculate the eigenvalues and eigenfunction of H0 of course we set the system in an "imaginary potential well of width L" so we have the...

A quick question from a high school student, In perturbation theory, what is to be done with the found energy correction? I'm working out the solution to an a/r+br potential and using br as the perturbation. I set up the integral and normalized, but what do I do with the expression that I'm...

if we know that the divergent series in perturbation theory of quantum field theory goes in the form: \sum_{n=0}^{\infty}a(n)g^{n}\epsilon^{-n} with \epsilon\rightarrow{0} then ..how would we apply the renormalization procedure to eliminate the divergences and obtain finite...

Let,s suppose we have a system H=H_{0}+\deltaH_{1} where we know how to solve H0 to obtain its eigenfunctions and energies now let,s apply perturbation theory in the form: E_{n}=E^{0}_{n}+<\psi_0|\delta{H_{1}}|\psi_0> but now we have that dH1 is so well behaved that gives us precisely the...

I'm reading the Cohen-Tannoudji book and I found somthing I don't understand in stationary perturbation theory. the problem the Hamiltonian is split in the known part an the perturbation: H=H_{o}+\lambda \hat{W} H_{o}|\varphi_{p}^{i}\rangle=E_{p}^{o}|\varphi_{p}^{i}\rangle (1) and...

Hi, I'm new to this subject, so bear with me. We consider the harmonic oscillator with a pertubation: \hat{H}' = \alpha\hat{p}. (What kind of a perturbation is that anyway, it's not a disturbance in the potential, what does it correspond to physically.) Now I have to calculate the...

Consider a particle confined in a two dimensional square well with faces at x=0,a;y=0,a. The doubly degenerate eigenstates appear as Psinp=(2/a)sin(n(pi)x/a)sin(p(pi)x/a) Enp=E1(n^2 + p^2) What do these energies become under perturbation H'=10^-3E1sin((pi)x/a)? Help...

I have been studying Perturbation theory in my Quantum class but my professor has not really explained why physically it comes into play. The book says that perturbation theory is used to help come up with approximate solutions to the Schrodinger Equation. Is this analagous to how we use Fourier...

Can anybody explain what Griffiths means when he talks about "good eigenstates" in degenerate time-independent purturbation theory? Mathematically, I know he is just talking about the eigen-vectors of the W matrix (where Wij = <pis_i|H'|psi_j>). But what do the eigen-vectors physically...

Consider the ground state of the hydrogen atom. Estimate the correction \frac{\Delta E}{E_1s} caused by the finite size of the nucleus. Assume that it is a unifromly charged shell with radius b and the potential inside is given by \frac{-e^2}{4\pi \epsilon b} Calculate the first order...

I was studying up on an aspect of perturbation theory, and I must have strained something (there's something about Hilbert spaces that I just can't get my head around...sorry, bad joke), because I have a really bad headache now. I was wondering what a headache is, and how we get them. I know...

For the harmonic oscillator V(x) = \frac{1}{2}kx^2, the allowed energies are E_n=(n+1/2)h \omega where \omega = \sqrt{k/m} is the classical frequency. Now suppose the spring constant increases slightly: k -> (1 + \epsilon)k. Calculate the first order perturbation in the energy. This is 6.2...

Hey there, I'm working on a perturbation theory problem, and I have no clue where to start in solving an infinite series. It's an infinite square well with a delta function potential in the centre and I'm trying to find the 2nd order energy correction to Energy En. Anyway, what I've got is...

I have a problem where I should calculate the ground state eigenfunction of a particle in the box where the potential V(x)=0 when 0<x<L and infinite everywhere else with the perturbation V'(x)=\epsilon when L/3<x<2L/3. I get that the total ground state eigenfunction with the first order...

Ok so I am trying to expand my understanding of these two concepts. Here is what I understand so far. There are very few Schrodinger Equations that are exactly solvable Both Theories are used to approximate a solution Perturbation Theory utilizes a similar function with a known solution and...

can somebody help me to find an expression for the density contrast (in fouruer space; delta_k) in a moving frame. Basically I am trying to figure out how various quantities like power spectrum P(k) etc., will look in a uniformly moving frame .

we have a particle in an infinite one-dimensional square well potential [V(x)=0 for 0<x<L and V(x) is infinite otherwise] and introduce a small potential (perturbation) in the middle of the square well potential. Then the first order energy correction for the ground state is 100 times...

Given a system, H = H_0 + V V is a small perturbation that does not depend on time. the system is in |E_0> at time t_0 H_0 |E_n> = E_n |E_n> H_0 |E_0> = E_0 |E_0> Let |\Psi(t)> be the solution of the system. Let |\Phi(t)> be the solution of the system without perturbation. Let...

consider a two fold degeneracy such that H Psi_a = E Psi_a and H Psi_b = E Psi_b and <Psi_a | Psi_b> = 0 All of the above are the unperturbed states, Hamiltonian and eigenvalue. Notice the two states share the eigen value E. Form the linear combination of the two states Psi = a *...

Here they go my doubts: a)Could It be that a theroy that is not renormalizable in three or four dimension could it be renormalizaed in two?..i mean if depending on the dimension a theory is renormalizable or not...when it comes to gravity..in which dimension is renormalizable?. b)When you...