I am thinking of: \begin{equation} \langle{\psi}|L|{\psi}\rangle \end{equation} $\psi$ is a complex function.

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    $\begingroup$ Hint: Is the angular momentum operator self-adjoint? $\endgroup$ – Qmechanic Nov 14 '19 at 18:27
  • $\begingroup$ No, it should be Hermitian but not self-adjoint... Still, I was thinking of L acting on an $\mathbf{L}^{2}$ function so I guess it should be real... $\endgroup$ – Yepman Nov 14 '19 at 21:00
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    $\begingroup$ @Yepman Why do you say that? Being an observable, angular momentum should be self-adjoint, not merely Hermitian. $\endgroup$ – J. Murray Nov 14 '19 at 23:49
  • $\begingroup$ I said that because I thought that L could be like p (momentum), and, being unbounded, it could have complex expectation values for some functions... But that is obviously not true for $\mathbf{L}^{2}$ wavefunctions. Thank you very much for your kind help. $\endgroup$ – Yepman Nov 15 '19 at 8:30

No. Expectation values of observable operators are always real.


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