# Can the angular momentum have complex expectation value?

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

• Hint: Is the angular momentum operator self-adjoint? – Qmechanic Nov 14 '19 at 18:27
• 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... – Yepman Nov 14 '19 at 21:00
• @Yepman Why do you say that? Being an observable, angular momentum should be self-adjoint, not merely Hermitian. – J. Murray Nov 14 '19 at 23:49
• 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. – Yepman Nov 15 '19 at 8:30