How Does Bohr's Hypothesis Predict Energy Levels in Harmonic Oscillators?

AI Thread Summary
Bohr's hypothesis states that a particle's angular momentum must be an integer multiple of h/2π, which can be applied to predict energy levels in a three-dimensional harmonic oscillator as E = lħω, where l = 1, 2, 3. The discussion highlights confusion about deriving this result from the standard energy equation for harmonic oscillators, E = 1/2 mv² + 1/2 kx². Participants seek guidance on the mathematical approach needed to connect these concepts. Additionally, there is curiosity about potential experiments that could falsify Bohr's predictions. Overall, the thread emphasizes the challenge of applying theoretical principles to practical scenarios in quantum mechanics.
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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?


Homework Equations





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
 
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Anyone able to help with this? Not sure how to proceed...
 
pleasseeeee?
 

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