Perturbation Definition and 378 Threads

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 -...

I just finished the first 4 chapters of Sakurai's Modern qm, and now I'm beginning to learn purterbation method and scattering theory, but from the feedback it seems that many people are quite unsatisfied with Modern qm on these parts. Could you guys recommand a nice book on perturbation and...

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 A particle of mass m in the infinite square well is subjected to the perturbation H'=Vo, 0<x<L/2, H'=0 else. (a) use first order perturbation theory to calculate the energies of the particle (b) what are the first order corrected wave functions? (c) if the particle is an...

Homework Statement I am given the hamiltonian, where H^{^}_{0} is that of the harmonic oscillator and the perturbation is (lambda)*(h-bar)*(omega)*[(lowering operator)^2 + (raising operator)^2]. I am asked to find the ground state, second-order approx. energy value. Homework...

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...

First order correction to particle-in-box eigenstates for Dirac perturbation Homework Statement Calculate the first three nonzero terms in the expansion of the correction to the ground state \psi^{1}_{1} for a Dirac delta perturbation of strength alpha at a/2 (box from 0 to a). Homework...

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...

I heard that there are semi-rigorous arguments that the sum of all (renormalized) terms in QED or QCD perturbation expansions do not converge, even though each term in the sum is systematically renormalized and rendered finite. This is suspected to be the case even if the coupling constant is...

Homework Statement Assume that the particle in the box is perturbed by a potential V_{1}(x) = x . Calculate the energy shift of the ground state and the first excited state in first-order perturbation theory. Homework Equations Unperturbed wave functions for the particle given by...

Homework Statement V(x) = \frac{1}{2}mw^{2}x^{2} + \lambdax^{4} Using first-order perturbation theory to calculate the energy shift of: 1. The ground state: \psi_{0}(x) = (2\pi\sigma)^{\frac{-1}{4}}\exp(\frac{-x^{2}}{4\sigma}) of the harmonic oscillator, where...

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...

Hi, I am having some problems understanding this concept, I hope you can help. I studied on Hobson, Efstathiou and Lasenby, in chapter 16 on Inflationary cosmology that in cosmological perturbation theory we need to express quantities in a gauge invariant way, very clear so far. The problem...

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...

Is it possible to describe the measurement process in QM simply as a perturbation to the system (either a small one or a very large one) so that effectively the eigenstates of the Hamiltonian evolve into eigenstates of an additional measuring operator? So at t=0 the Hamiltonian H turns into...

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...

Is it possible to write down a statement about the asymptotic behaviour of the wave function after a small perturbation has been switched on? So I have and initial wave function \psi_0 and the Hamiltonian H=\begin{cases} H_0 & t<0\\ H_0+V+R & t\geq 0 \end{cases} where V is a small perturbation...

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)}...

Hi, I know that for degenerate states, we need to apply degenerate perturbation theory by looking at the perturbative hamiltonian in the subspace of the degenerate states. What then if the states still degenerate after we cast them the generate subspace. Is there a way to find the zero...

Am I correct in thinking string theory has an infinite number of terms so to prove finiteness to the first order means proving one (or the first) term to be finite? If so, then how can we ever prove an infinite number of terms? And what exactly does it mean to say, or prove, something is...

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...

Hi, I have been trying to model the temperature distribution along the length of a fin. With a constant 'h', the analytical solution is easy to get. But in my case, near the tip, the value of h changes significantly. Is perturbation a good technique to get a analytical solution in...

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...

Hi, there! I'm trying to understand the derivation of (linearized) pertubation equations given in my lecture. As usual the density and velocity fields are split into a homogeneous and an inhomogeneous part: \rho(t,x) = \rho_0(t) + \delta \rho(x,t) \vec{v}(t,x) = \vec{v_0}(t) +...

Homework Statement Find the perturbation approximation of the following in terms of powers of θ0. T=\sqrt{\frac{8L}{g}}\int^{\theta_0}_{0} \frac{d\theta}{\sqrt{cos\theta - cos\theta_0}} It is helpful to first perform the change of variable u = θ/θ0 in the integral Homework Equations...

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 I'm just working through a textbook and there's a line in which I'm clearly missing something. What I want to do is show that from: [tex] \bar{h^{TT}_{\mu \nu}} = A^{TT}_{\mu \nu} cos(\omega (t-z)) [\tex] to [tex] h^{TT}_{\mu \nu} = B^{TT}_{\mu \nu} cos(\omega (t-z))...

Homework Statement Given: \mathbf{H}=V_0\begin{bmatrix} 1-\epsilon & 0 & 0\\ 0 & 1& \epsilon\\ 0 & \epsilon & 2 \end{bmatrix} \epsilon<<1 a) Find eigenvalues and eigenvectors of the unperturbed Hamiltonian (\epsilon=0) b) Solve for eigenvalues of the Perturbed Hamiltonian...

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, I'm a geologist, and I really suck in physics so I would need some help, please! This is not a homework question, I'm an academic! This is for my research... Let's say I have a "box" (a river catchment) with a mass, M, of material (sediments) in this box, which resides in the box for a...

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...