Expectation of an Hermitian operator is real.

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Homework Statement

WTS \langle \hat{A} \rangle = \langle \hat{A} \rangle^\ast

The Attempt at a Solution

\langle \hat{A} \rangle^\ast = \left(\int \phi_l^\ast \hat{A} \phi_m dx\right)^\ast=\left(\int (\hat{A}\phi_l)^\ast \phi_m dx\right)^\ast= \int \phi_m^\ast \hat{A}\phi_l dx. So far, I haven't seen why this equals \int \phi_l^\ast \hat{A} \phi_m dx.

Thanks

 

[mjsd]

use same fields to show
eg. (\Psi, A\Psi) = (\Psi, A\Psi)^*