1. The problem statement, all variables and given/known data Consider the one-dimensional harmonic oscillator of frequency ω0: H0 = 1/2m p2 + m/2 ω02 x2 Let the oscillator be in its ground state at t = 0, and be subject to the perturbation Vˆ = 1/2 mω2xˆ2 cos( ωt )at t > 0. (a) Identify the single excited eigenstate of H0 for which the transition amplitude is nonzero in first-order time-dependent perturbation theory. Calculate this amplitude explicitly. (b) Calculate the dominant term of the first-order transition probability to the state identified in (a) for ω = 2ω0. Give a condition for which this result becomes meaningless. 2. Relevant equations H = H0 + V 3. The attempt at a solution Used the above equation to start my solution ended up with something in the form of H = p2/2m + m/2 (ω02 + ω2cos( ωt )) x2 I am unsure as to how to keep going and find the eigenstates of H0. I thought it was more intuitive to solve for the eigenstates of H not H0. And I'm also not quite sure how to find the transition amplitude. Any help is greatly appreciated.