Bohr Quantization Rule for Angular Momentum

[Tipler5]

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.

 

[Tipler5]

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.

 

[Troels]

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

$$hf= E_{n2}-E_{n1}$$


Now insert the energy levels of the harmonic oscillator and the relation between $$f$$ and $$\lambda$$ and the answer should be obvious.