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!

Hyperfine Hamiltonian

  1. May 17, 2009 #1

    TFM

    User Avatar

    1. The problem statement, all variables and given/known data

    Derive the hyperfine Hamiltonian starting from [tex] \hat{H}_H_F = -\hat{\mu}_N \cdot \hat{B_L} [/tex]. Where [tex] \hat{\mu}_N [/tex] is the magnetic moment of the nucleus and
    [tex] \hat{B_L} [/tex] is the magnetic field created by the pion’s motion around the nucleon. Write down the Hamiltonian in the form [tex] \hat{H}_H_F = ... \vec{I} \cdot \vec{L} [/tex].

    2. Relevant equations

    [tex] \hat{B_L} = \frac{\mu_0e}{4\pi r^3}\vec{r} \times \vec{v}[/tex]

    3. The attempt at a solution

    Okay, I have tried putting everything together, and so far I currently have:

    [tex] \hat{H}_{hf} = g_n \mu_n \frac{\vec{I}}{\hbar}\cdot \frac{-\mu_0e}{4\pi r^3} \times V [/tex]

    but I am not sure where to go from here. Any suggestions?

    TFM
     
    Last edited: May 18, 2009
  2. jcsd
  3. May 17, 2009 #2
  4. May 18, 2009 #3

    TFM

    User Avatar

    Thanks for the linkj.

    I was koooking through my notes as suggested in the script, and they have a different version, my notes have [tex] \hat{H}_{HF} = -\hat{\mu}_N\hat{B}_j [/tex]

    the notes then go on to say that Bj is parallel to j

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




Similar Discussions: Hyperfine Hamiltonian
  1. The Hamiltonian (Replies: 9)

  2. Hyperfine Interaction (Replies: 5)

Loading...