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

Homework Help: Zeeman effect and lande g factor

  1. Nov 3, 2008 #1

    KFC

    User Avatar

    1. The problem statement, all variables and given/known data
    Deduce the expression of Lande g factors from Zeeman effect


    2. Relevant equations
    For Zeeman effect, we treat the energy perturbation as [tex]\vec{S}\cdot\vec{L}[/tex], where [tex]S[/tex] is the spin and [tex]L[/tex] is the orbital momentum. Let magnetic field along z direction so the energy correction would be

    [tex]\langle jm|J_z + S_z|jm\rangle[/tex]


    3. The attempt at a solution
    I try to write

    [tex]\vec{S}\cdot\vec{L} = \dfrac{1}{2}(\vec{J}^2 + \vec{S}^2 - \vec{L}^2)[/tex]

    The solution would be
    [tex]g = 1 + \dfrac{j(j+1) + s(s+1) - l(l+1)}{2j(j+1)}[/tex]

    The above expression [tex]\vec{S}\cdot\vec{L}[/tex] gives the numerator of the second term of the solution, but how to get the denormenator? How to connect the [tex]\vec{S}\cdot\vec{L}[/tex] with [tex]J_z + S_z[/tex]?
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted