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QM: Expectation value relation

  1. Jul 25, 2012 #1
    1. The problem statement, all variables and given/known data

    My book uses the following in a calculation
    \left\langle a \right\rangle \left\langle {b^\dagger } \right\rangle + \left\langle {a^\dagger } \right\rangle \left\langle b \right\rangle = 2\operatorname{Re} \left[ {\left\langle a \right\rangle \left\langle {b^\dagger } \right\rangle } \right]
    where a and b are QM operators. I agree with the relation [itex]z^*+z=\text{Re}(z)[/itex] (for z a complex variable), but in the above case the conjugation is on the operator, not the expectation value itself. Is the relation valid?

    Last edited: Jul 25, 2012
  2. jcsd
  3. Jul 25, 2012 #2
    Ahh, I see it now. The relation is valid, as <b^+> = <b>*.
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