(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle of mass m is confined in a two-dimensions by the potential energy V = 1/2k(x^{2}+4y^{2}). Write down the Schrodinger equation for the system. Write down the ground state wave function and find the lowest four energy levels in terms of the quantities ħ, k, m etc. Make clear which, if any, of the levels is degenerate. Use any of the results you need from the one-dimensional harmonic oscillator without proof.

2. Relevant equations

Schrodinger's equation, two-dimensional:

[(-ħ/2m)(d^{2}/d^{2}x + d^{2}/d^{2}y) + V(x)] [itex]\psi[/itex]_{E}(x,y)]=E [itex]\psi[/itex]_{E}(x,y)

One-dimensional harmonic oscillator equations:

[itex]\psi[/itex]_{0}= (m[itex]\omega[/itex]_{0}/ħ[itex]\pi[/itex])e^{-ax2}

[itex]\omega[/itex]_{o}=[itex]\sqrt{k/m}[/itex]

a=[itex]\sqrt{km}[/itex]/2ħ

E_{n}= (n+1/2)ħ[itex]\omega[/itex]_{0}

3. The attempt at a solution

Schrodinger's equation:

[(-ħ^{2}/2m)(d^{2}/d^{2}x + d^{2}/d^{2}y) + 1/2k(x^{2}+4y^{2})] [itex]\psi[/itex]_{E}(x,y)=E[itex]\psi[/itex]_{E}(x,y)

After this I'm not really sure what to do. As for what to plug in where, and how to solve for the energy levels. Do I use the equation to solve for the energy levels? How?

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# Solving 2-D Schrodinger Equation?

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