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Homework Help: Problem with solving the Colatitude equation

  1. Apr 24, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that the priciple quantum number n limits the values of the angular momentum quantum number l such as

    l <= n-1

    Calculate the degeneracy of energy levels of the hydrogen atom when only the Colomb force is taken into account.

    The attempt at a solution
    I wrote the 3D-Schrödinger equation (in spherical coordinates) and solved it by seperating the variables in the form

    Psi(r,phi,theta) = R(r) * P(theta) * F(phi) -> so i have 3 equations for 3 quantum numbers.

    Then I solved the azimuthal equation to get to constant Cphi, which is

    Ctheta = -ml^2 (ml.. magnetic quantum number)

    So I have now the Colatitude equation:

    sin(theta)/P * d/dtheta [ sin(theta) dP/dtheta] + Cr sin^2(theta) = -Cphi with Cphi = -ml^2

    So far I'm right, I think..

    I know that, if I solve this equation it will show that "l <= n-1". I also know that I have to do this by using polynomial expansion.
    But I don't know how to do this here.

    I hope somebody can help me! Thx
  2. jcsd
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