\begin{equation}
E_{v}=\hbar\omega(v+\frac{1}{2})+\frac{1}{24}V_{4}\left\langle v\left|x^{4}\right|v\right\rangle -\frac{V_{3}^{2}}{36}\left[\frac{\left|\left\langle v\left|x^{3}\right|v+1\right\rangle \right|^{2}-\left|\left\langle v\left|x^{3}\right|v-1\right\rangle \right|^{2}}{\hbar\omega}+\frac{\left|\left\langle v\left|x^{3}\right|v+3\right\rangle \right|^{2}-\left|\left\langle v\left|x^{3}\right|v-3\right\rangle \right|^{2}}{3\hbar\omega}\right]
\end{equation}