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!

Spin 1/2 in B-field polarization direction?

  1. Apr 27, 2007 #1
    spin 1/2 in B-field polarization direction?!?!

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

    A spin 1/2 particle with magnetic momnet mu=mnot*sigma is placed in

    uniform B-field, where the magnetic field is pointing in (theta,phi) direction

    in spherical coordinates

    At t=0, the particle is in the (1 0) state, i.e. sigma(z)=1 and the polarization

    direction is =e3 (z hat direction).

    Find out the polarization direction of the particle at t>0.



    2. Relevant equations

    the theory of spin is like angular momentum

    magnetic moment mu=-gamma*S

    S=spin matrix

    S^2|sm>=hbar^2s(s+1)|sm>

    and Sz|sm>=hbar*m|sm>


    3. The attempt at a solution

    Not sure how to approach this one, i assume that the particle is at rest in the B-field

    the Hamiltonian for a spinning charged particle in B-field is H=-gamma*(B dot S)

    this is a time-DEPENDENT perturbation

    how can i realte what is given to the polarization direction?

    cheers
    nate:biggrin:
     
  2. jcsd
  3. Apr 28, 2007 #2
    ok, let me try this again

    H=-mu*B (this is the interaction energy between spin and B-field)

    for a particle of spin 1/2, with magnetic moment mu=mu(s)*S

    the Hamiltonian is h=1/2*m(p-q/c*A)^2-mu*B

    B=BX+BY+BZ (where i need to put B into spherical coordinates)

    so if i have the B-field in the z-direction, A=(-By,0,0)

    so....

    H=1/2*m[(px^2+py^2+pz^2)+(2*q*B*px/c)*y+(qB/c)^2*y^2]-(mu*B/S)Sz

    is this correct? i have a Hamilton with Sz in it which is given as sigma(z)=1 (pauli spin matrix)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?