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

Potential of a simple harmonic oscillator is[itex] \frac{1}{2}m\omega

^{2}(x^{2}+4y^{2})[/itex].Find the energy eigenvalues?

2. Relevant equations

Seperation of variables,i think. But i got stuck in the midway.

3. The attempt at a solution

[tex]\frac{-\hslash ^{2}}{2m}\left( \frac{\partial ^{2}\psi }{\partial x^{2}}+%

\frac{\partial ^{2}\psi }{\partial y^{2}}\right) +\frac{1}{2}m\omega

^{2}(x^{2}+2y^{2})\psi =E\psi [/tex]

[tex]\psi (x,y)=X(x)Y(y)[/tex]

[tex]\frac{\partial ^{2}X}{\partial x^{2}}-\frac{m^{2}}{\hslash ^{2}}\omega

^{2}x^{2}X+\frac{2m}{\hslash ^{2}}E_{1}X=0[/tex]

[tex]\frac{\partial ^{2}Y}{\partial x^{2}}-\frac{2m^{2}}{\hslash ^{2}}\omega

^{2}y^{2}Y+\frac{2m}{\hslash ^{2}}E_{2}Y=0[/tex]

need a hint about how to proceed.

Thanks.

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# 2 dimensional harmonic oscillator.find the energy eigenvalues?

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