Our method Wang et al. [5] The states $|{\psi }_{n}〉$ $\begin{array}{c}|{}^{\left(1a\right)}\psi {}_{n}\left(t\right)〉={\text{e}}^{\frac{-i{}^{\left(1a\right)}E{}_{n}t}{\hslash }}\left[{k}_{-4}|n-4〉+{c}_{-3}|n-3〉+{k}_{-2}|n-2〉\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+{c}_{-1}|n-1〉+{c}_{+1}|n+1〉+{k}_{+2}|n+2〉\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+{c}_{+3}|n+3〉+{k}_{+4}|n+4〉+|n〉\right]\end{array}$ $\begin{array}{c}|{\phi }_{n}〉=|n〉+A\left(n\right)|n-1〉+B\left(n\right)|n+1〉\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+C\left(n\right)|n-2〉+D\left(n\right)|n+2〉\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+E\left(n\right)|n-3〉+F\left(n\right)|n+3〉\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+G\left(n\right)|n-4〉+H\left(n\right)|n+4〉\end{array}$ Quasi-energies $\begin{array}{c}{}^{\left(2a\right)}E{}_{n}=\hslash {\omega }_{0}\left(n+\frac{1}{2}\right)+{\mu }_{2}\frac{3}{4}\hslash {\omega }_{0}\left(2{n}^{2}+2n+1\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-{\mu }_{1}^{2}\frac{15\hslash {\omega }_{0}}{4}\left({n}^{2}+n+\frac{11}{30}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-{\mu }_{2}^{2}\frac{\hslash {\omega }_{0}}{8}\left(34{n}^{3}+51{n}^{2}+59n+21\right)\end{array}$ $\begin{array}{c}{E}_{n}=\hslash {\omega }_{0}\left[\left(n+\frac{1}{2}\right)-{\left(\frac{{\alpha }_{w}}{\hslash {\omega }_{0}}\right)}^{2}{A}_{n}^{\left(2\right)}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\frac{{\beta }_{w}}{\hslash {\omega }_{0}}{B}_{n}^{\left(1\right)}-{\left(\frac{{\beta }_{w}}{\hslash {\omega }_{0}}\right)}^{2}{B}_{n}^{\left(2\right)}\right]\end{array}$