- #1

MathematicalPhysicist

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## Homework Statement

1. A particle of mass M is in a square well, subject to the potential:

[tex]V(x)= V0\theta(x-a/2)[/tex] 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 particle is moving in a two dimensional harmonic oscillator with perturbation [tex]\delta V=\lambda x^2 y^2[/tex] For the ground state and the first excited state, find the first order correction to.

## Homework Equations

## The Attempt at a Solution

1. As I see it the hamiltonian has a perturbation in x in [a/2,a), which is V0.

, but from the equation for the second order correction to the energy which is:

[tex]\sum_{m doesn't equal n} \frac{|<m|V0|n>|^2}{E_n-E_m}[/tex], where [tex]E_k=\frac{(\hbar k)^2}{2M}+V_0[/tex], so that means the second order correction is zero cause <m|n> for m not equal n equlas zero, doesn't make sense to me, what am I missing?

For 2, for the first excited state I get that it's degenrate, cause [tex]E_{1,0}=E_{0,1}[/tex], not sure how to find for the first excited state its first order correction.

P.S

I sent an email to the TA with my questions, so far he hasn't replied, this is why I am asking here.