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Spin orbit coupling

  1. Feb 25, 2013 #1
    I have a question about how my book derives a formula. It starts with:
    We have an electron free too move on a cylinder and from the cylinder there is an electric field pointing radially outwards.
    Now for an electron moving in an electric field it sees local magnetic field given by:

    B = 1/c^2 v x E (1)
    And from spin pertubation theory we now get the following pertubation of the Hamiltonian:
    H' = -μ [itex]\bullet[/itex] B = C L[itex]\bullet[/itex]S

    I don't understand the last equality. I know μ(the magnetic moment) is proportional to the spin but how do we get L from (1)? - and how does it even make sense to use "v" the velocity in classical electrodynamics in a quantum mechanical system?
  2. jcsd
  3. Feb 25, 2013 #2


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    Science Advisor

    I would argue like this: use ## v=i\hbar [H,\vec{r}]## (holds also quantum mechanically), express ## \vec{r} ## in polar coordinates and use ##H=L^2/2mr^2##.
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