How to Solve the Schrödinger Equation for a 3D Isotropic Harmonic Oscillator?

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Homework Statement




solve the schrodenger equation for the3-D isotropic harmonic oscilator by sepration of varibals in sphericalpolar coordenates.

Homework Equations




The Attempt at a Solution

 
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ok, attempt to solution?

(there is a discussion on this in many textbooks, such as the nuclear shell model by Heyde)
 
for a start, find out what the laplacian is in spherical coords and expand the shrodinger equation. from there you need to separate your variables. remember also that your potential energy is a certain expression if you dealing with a harmonic oscillator.
 

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