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Homework Help: Semiclassical approach

  1. Mar 10, 2010 #1
    1. The problem statement, all variables and given/known data

    I have potential hole from a to b. This potential hole is sum of U(r) (bounded function) and l(l+1)/r^2, where l is azimuthal quantum number. In my book about semiclassical approach is written: if [tex]n_{r}[/tex] >>1 then in rules of quantization in basic range of integration centrifugal potential is correct with order of magnitude is
    [tex]\frac{(l+1/2)^{2}}{n^{2}_{r}}[/tex]. I cant undrstand, why it so

    2. Relevant equations

    [tex]\int\sqrt{2(E-U(r)-\frac{l(l+1)}{2r^{2}})}[/tex] = [tex]n_{r}[/tex]+[tex]\gamma[/tex] Bohr's rules of quantization

    [tex]\frac{l(l+1)}{2r^{2}}[/tex] centrifugal potential


    3. The attempt at a solution
    I try to prove it so: i investigate difference between two integrals: one of them include centrifugal potential, other no. But i cant obtain this formula. I am sure, this formula obtain very easy, but i dont no how. Have you got any ideas?

    P.S sorry my english
     
    Last edited: Mar 11, 2010
  2. jcsd
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