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QM: spin

  1. May 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the eigenvalues and eigenstates of the spin operator S of an electron in the direction
    of a unit vector n; assume that n lies in the xz plane.

    2. Relevant equations

    S|m>= h m|m>

    3. The attempt at a solution

    This question is from Zettili QM and they have written:

    n.S|m>= (h/2) m|m>

    I do not understand why are they taking a half.
    If I take m=1/2 in S|m>= (h/2) m|m>, I get h/4 but the answer should be h/2, by using S|m>= h m|m>.
    So where am i going wrong?
  2. jcsd
  3. May 18, 2013 #2


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    m is the quantum number. you need to check its definition
  4. May 18, 2013 #3
    Of course it is a quantum number but why is there a half?
  5. May 18, 2013 #4


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    Staff Emeritus
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    It's probably just a typo. It doesn't really matter, though. It just means the quantum numbers are ##\pm1## instead of ##\pm 1/2##.
  6. May 18, 2013 #5


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    I see now. The notation in the two equations is not consistent.
    S|m>= h m|m>
    n.S|m>= (h/2) m|m>
    In the second equation, m is a 'quantum number' (i.e. integer), while in the first equation I guess you could interpret m as the value of the projection of angular momentum, in natural units.
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