[QUE/QM-08004]

Let \(|n\rangle\) denote the \(n^\text{th}\) excited state of a harmonic  oscillator. Show that   \begin{equation*}       \langle n| x |m\rangle= \sqrt{\frac{\hbar}{2m\omega}}\Big(  \sqrt{n+1}\delta_{m, n+1} + \sqrt{n}\delta_{m, n-1} \Big)       \end{equation*}