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Homework Help: Quantizing the oscillator. I'm having trouble getting a real number for the velocity

  1. Oct 5, 2011 #1
    1. The problem statement, all variables and given/known data

    Use Bohr's rule, L=n[itex]\hbar[/itex], to find the quantized speeds, radii, and energies for circular orbits of a particle of mass m bound to the origin by the Hooke's-law force, F(r) = -Kr.


    2. Relevant equations

    mass=m

    ƩF=ma

    F(r)=-kr

    L=n[itex]\hbar[/itex]

    p=mvr

    mvr=n[itex]\hbar[/itex]

    r=n[itex]\hbar[/itex]/mv (a)

    3. The attempt at a solution

    mv²/r=-kr

    mv²=-kr² (b)

    subbing (a) into (b)

    mv²=-kn²[itex]\hbar²[/itex]/m²v²

    solving for v...

    (v²)²=-kn²[itex]\hbar²[/itex]/m³

    v=(-kn²[itex]\hbar²[/itex]/m³)^¼

    and this is where I get stuck because of the negative sign in the 4th root of v. If I make ma=kr it works out, BUT it seems cheap just to change the law from -kr to kr.
     
    Last edited: Oct 5, 2011
  2. jcsd
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