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Precessing electron, probability of spins

  1. Mar 1, 2008 #1
    1. The problem statement, all variables and given/known data

    An electron precesses in B field aligned with +z axis. At t=0, spin of the electron is in the +x direction. Wave function is given as a matrix, but is equal to 1/sqrt(2)[e^-iwt/2 |z> + e^iwt/2 |-z> ]. (Sorry, idk LaTeX). For t>0, find the probability of finding the electron in the state:

    (a) ms = +h/2 [h-bar] [m sub s]
    (b) msx = +h/2 [h-bar] [m sub sx]

    2. Relevant equations



    3. The attempt at a solution

    Actually, I just want to make sure I set these problem up right. I have the answers, and I did get the correct answers, but:

    for (a): I did |<z|psi>|^2, it came out to 1/2
    for (b): I did |<x|psi>|^2, it came out to cos^2(wt/2)

    I'm not sure if my setup for (a) was right, or not. I could've got the same result with |<-z|psi>|^2, for example. I'm not sure if its a notation thing with the book, they tend to use msx and msy, but I don't recall seeing msz, perhaps they use the notation that msz = ms. This makes some sense, as there is no such thing as definite total spin, even with just 1 electron.
     
  2. jcsd
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