Bohr Quantization Rule for Angular Momentum

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Use the Bohr quantization rules to calculate the energy levels for a harmonic oscillator, for which the energy is p²/2m + mw²r²/2; that is, the force is mw²r, where w is the classical angular freq of the oscillator. Restrict yourself to circular orbits.
So far I have that mvr=nh\, w=v/r, and p=mv. I cannot get it into the form E=(n+1/2)h\w. Please help!

What is the analog of the Rydberg formula for 1/λ of the radiation emitted when the particle jumps from level n2 to n1?
Not sure what it is asking.
 

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Use the Bohr quantization rules to calculate the energy levels for a harmonic oscillator, for which the energy is p²/2m + mw²r²/2; that is, the force is mw²r, where w is the classical angular freq of the oscillator. Restrict yourself to circular orbits.

So far I have that mvr=nh\, w=v/r, and p=mv. I cannot get it into the form E=(n+1/2)h\w. Please help!

What is the analog of the Rydberg formula for 1/λ of the radiation emitted when the particle jumps from level n2 to n1?
Not sure what it is asking.
 
  • #3
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2
What is the analog of the Rydberg formula for 1/λ of the radiation emitted when the particle jumps from level n2 to n1?
Not sure what it is asking.

You're asked, I think, to write down the relation for the waveleght of radiation emitted from (or absored by) a harmonic oscillator when it transists from one state to another.

The Rydberg formula originates from the relation

[tex]
hf= E_{n2}-E_{n1}
[/tex]


Now insert the energy levels of the harmonic oscillator and the relation between [tex]f[/tex] and [tex]\lambda[/tex] and the answer should be obvious.
 
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