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1. The problem statement, all variables and given/known data

A 2-D harmonic oscillator has an energy Ensubxnsuby and wavefunctions [tex]\phi[/tex]nsubxnsuby

The first excited states are 2-fold degenerate E[tex]_{01}[/tex]=E[tex]_{10}[/tex]=2[tex]\hbar[/tex][tex]\omega[/tex]

What are the energies and wavefunctions if we add the perturbation

H'=gwyp[tex]_{x}[/tex]?

2. Relevant equations

En=[tex]\hbar[/tex][tex]\omega[/tex](nx + ny + 1)

[tex]\phi[/tex]subnxny=[tex]\phi[/tex]subnx(x)[tex]\phi[/tex]subny(y)

H=g[tex]\omega[/tex]yPsubx

3. The attempt at a solution

I'm unsure exactly how to approach this problem, and I think it's a combination of not knowing exactly how to work with this perturbation and never having dealt with 2-D Harm. Osc. I suppose for the energies just a simple degenerate calculation of the three matrix elements of H' (where I come to trouble working with the ypsubx) and then plugging in for the two fold degeneracy equation. The wavefunctions would be a similar sum over H'mn m!=n. Also I know the wavefunctions (just nx and ny of 1-D 0 and 1 states multiplied together), just don't know where to go from here. Any help would be appreciated. THanks

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# Homework Help: 2-D Harmonic Osc. with Perturbation

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