Calculate the evolution operator for the interaction picture in the case in exercise 4.

Data From Exercise 4:-

Consider a harmonic oscillator perturbed by \(H_{1}=\lambda\left(a+a^{\dagger}\right)^{3}\). Write down the explicit evolution equations for states (the first two terms in the expansion in \(\omega\) ) and the \

(a, a^{\dagger}\) operators in the interaction picture.