1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?

Similar Discussions: Problem with solving the Colatitude equation
  1. Lagrangian problem (Replies: 0)

  2. Problem is. (Replies: 0)