Consider a harmonic oscillator perturbed by (H_{1}=lambdaleft(a+a^{dagger} ight)^{3}). Write down the explicit evolution equations for states (the

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.