Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Central Potential Problem

  1. May 21, 2005 #1
    How can I calculate the AM and energy of each level in a resulting multiplet of a particle of spin=1/2 with orbital AM quantum number, L=2 subject to a spin orbit potential,
    i am at my wits end! :cry: :cry: :cry:
  2. jcsd
  3. May 21, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper


    [tex] \hat{\vec{J}}=\hat{\vec{L}}+\hat{\vec{S}} [/tex]

    Use the C-G theorem to generate the irreducible spaces and the C-G formula to find the basis in such spaces.
    Then,once u got the basis,then,using perturbation theory for a nondegenerate energy level

    [tex] \Delta E^{(1)} =\langle n,j,m_{j} |\hat{V}|n,j,m_{j}\rangle [/tex]

  4. May 21, 2005 #3
    Cheers mate, I can do it now.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook