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QM: Expectation values of spin

  1. Oct 5, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    The expectation value for S_x (spin in x-direction) is:

    \left\langle {S_x } \right\rangle = \left\langle {\phi |S_x \phi } \right\rangle = \phi ^\dag S_x \phi
    where \phi is the state and \phi^"sword" is the hermite conjugate.

    My question is: I thought that when finding expectation values, you are supposed to complex conjugate the left part of the inner product, not hermite conjugate?
  2. jcsd
  3. Oct 5, 2008 #2


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    Gold Member

    I am fairly certain that by definition,


    so in a way it's the same thing (T is the transpose matrix)
  4. Oct 6, 2008 #3
    I get it - thanks :-)
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