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Bohr Quantization Rule for Angular Momentum

  1. Jan 22, 2008 #1
    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.
     
  2. jcsd
  3. Jan 22, 2008 #2
    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.
     
  4. Jan 23, 2008 #3
    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.
     
    Last edited: Jan 23, 2008
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