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I want to ask how to solve the equation $$-\frac{{\hbar}^{2}}{2m}\frac{\partial}{\partial_{r}^{2}}u(r)=(E-\frac{1}{2}Kr^{2})u(r)$$ with $K$ being a constant.

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I admit this problem is really intro level... –  Kerry Mar 18 '11 at 5:28
    
fisica.net/quantica/quantum_harmonic_oscillator_lecture.pdf I found that pdf by a quick search. I think that pdf gives a pretty good answer from a physics perspective. –  svenkatr Mar 18 '11 at 5:44
    
Thanks! This is very helpful. –  Kerry Mar 18 '11 at 6:28
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