The expectation value of ${p^2\over 2m}$ in eigenstate

The expectation value of ${p^2\over 2m}$ is

$$\begin{eqnarray*} \langle u_n\vert{p^2\over 2m}\vert u_n\rangle &=&{-1\over 2m}... ...n\rangle \\ &=&{\hbar\omega\over 4}((n+1)+n)={1\over 2}E_n \\ \end{eqnarray*}$$

(See the previous section for a more detailed computation of the same kind.)