The expectation value of $p$ in eigenstate

(See the previous example is you want to see all the steps.) The expectation value of $p$ also gives zero.

$$\bgroup\color{black} \langle u_n\vert p\vert u_n\rangle=-i\sq... ...a\over 2}\langle u_n\vert A-A^\dagger\vert u_n\rangle=0 \egroup$$