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humanist rho
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Homework Statement
Potential of a simple harmonic oscillator is[itex] \frac{1}{2}m\omega
^{2}(x^{2}+4y^{2})[/itex].Find the energy eigenvalues?
Homework Equations
Seperation of variables,i think. But i got stuck in the midway.
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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