Derivation of energy levels in a quantum harmonic oscillator, ##E=(n+1/2) \hbar\omega##, is long, but the result is very short. At least in comparision with infinite quantum box, this result is simple. I suspect that it can be derived avoiding Hermite polynomials, eigenvalues, etc. I understand them, but I think that short results are many times a consequence of short derivations.(adsbygoogle = window.adsbygoogle || []).push({});

I found something, what can avoid this:

http://ocw.mit.edu/courses/nuclear-...s-fall-2012/lecture-notes/MIT22_51F12_Ch9.pdf

It seems that in pages 80 and 81 in sec. 9.1.2 is something, what maybe avoid this.

For beginning, I do not understand, why

##N(a|n>)=(n-1)(a|n>)## gives that

##a|n=c_n|n-1>##

Eigenvalue becomes eigenfunction.

Probably this is an easy question, but I will help for further derivation.

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# I Simple calc. of energy levels in quantum harmonic oscillator

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