A ID harmonic oscillator of angular frequency w and charge q is in its ground state at time t=0. A perturbation H'(t) = qE eA3 (where E is ekctric field and ß is a constant) is %3D applied for a time t = t. Cakulate the probability of transition to the first and second excited state. (hint: you may expand exponential in perturbation and keep it only up to linear term)

A ID harmonic oscillator of angular frequency w and charge q is in its ground state at time t=0. A perturbation H'(t) = qE eA3 (where E is ekctric field and ß is a constant) is %3D applied for a time t = t. Cakulate the probability of transition to the first and second excited state. (hint: you may expand exponential in perturbation and keep it only up to linear term)