Expectation Value of Operator A: c or Complex Conjugate?

[dyn]

If I have the following expectation value for a general operator A < psi | cA | psi > where c is a complex constant and I want to take c outside the bracket does it go as c or its complex conjugate ?

 

[king vitamin]

If I have the following expectation value for a general operator A < psi | cA | psi > where c is a complex constant and I want to take c outside the bracket does it go as c or its complex conjugate ?

You take c outside, and do not complex-conjugate it. You can always view the bra <psi| as a linear operator on kets, and since A|psi> is a ket bringing c outside is fine. Almost all operations in QM are linear, and complex constant can be taken outside of linear operators. When you deal with time-reversal, you introduce anti-linear operators where you do have to complex-conjugate constants to bring them outside, but this is not the case here.