Answer by joshphysics for Expectation value of an operator
Assuming $|\psi_1\rangle$ and $|\psi_2\rangle$ are orthonormal, your equation after you write "I found" is incorrect, it should be\begin{align} (\langle \Psi|\hat Q)(\hat Q|\Psi\rangle) &=...
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Suppose we have:$$\hat{Q}|\psi_1\rangle=q_1|\psi_1\rangle \\\hat{Q}|\psi_2\rangle=q_2|\psi_2\rangle$$with $q_1 \neq q_2$.Then consider the...
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