[QUE/QM-08009]

Compute average of kinetic and potential energies     \[  \text{K.E.} = \frac{p^2}{2m},\qquad \text{P.E.}=  \frac{1}{2}m\omega^2x^2.\]   in the \(n^\text{th}\) excited state and show that the the average of total   energy is \(\frac{1}{2}\hbar \omega\).