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

1D Potential V(x) = mw^2x^2/2, part of a harmonic oscillator.

Suppose that the spring can only be stretched, so that the potential becomes V=infinity for x<0. What are the energy levels of this system?

2. Relevant equations

3. The attempt at a solution

I argued my way though this problem by the following:

We know that V(x) = infinity

V(0) = 0

V(x) = 0 otherwise

From our typical energy levels we know E_n = ħw(n+1/2) for n=0,1,2,3,...

But there is a barrier at x =0. Therefore we need x=0 to have E=0.

Energy levels are thus:

E_n = ħw(n+1/2) with n=1,3,5,7,...

One can see this though the wave function graphs: https://i.stack.imgur.com/rb340.gif

Is that argued properly? Did I find the right solution?

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# Homework Help: QM: 1D Potential Well Spring - Energy Levels

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