Verifying Bohr's Hypothesis for 3-D Harmonic Oscillator

[bon]

1. Homework Statement

Show that bohr's hypothesis (that a particle's angular momentum must be an integer multiple of h/2pi) when applied to the three dimensional harmonic oscillator, predicts energy levels E=lh/pi w with l = 1,2,3. Is there an experiment that would falsify this prediction?


2. Homework Equations



3. The Attempt at a Solution

Hmm not sure how to approach this..

So for a harmonic oscillator E = 1/2 m v^2 + 1/2 k x^2...but how do i arrive at their result!?

Also what experiment would falsify?

Thanks

 

[vela]

Start by figuring out what the potential V(x,y,z) of the 3D harmonic oscillator is, and from that, you can determine what force acts on the mass. Then it's pretty much the same derivation as for the Bohr model of the atom except you have a different force to plug into F=ma.

By the way, are you missing a factor of 2 in the expression for the energy? I think it should be E=l(h/2π)ω.