Is the Expectation Value Relation for QM Operators Valid?

[Niles]

Homework Statement

Hi

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 $z^*+z=\text{Re}(z)$ (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?Niles.

 

[Niles]

Ahh, I see it now. The relation is valid, as <b^+> = <b>*.