Answer Happy

3. A particle of mass m is initially in the ground state (Eo) of a potential V = 1k2². From t = 0 to t = T₁ the system is subject to the perturbation: = ħm31 (2) where p is the linear momentum of the particle, wo = √k/m, po = √hmwo, and a is a small unitless parameter. T is assumed to be small enough that the perturbation of the ground state is still small at time T. (a) (15 points) Find the probability that at time T the system is found in the unperturbed first excited state. (b) (10 points) Assuming T is small so that the perturbation is still small, and that the particle starts in the ground state, to which states is there a non-zero probability of a direct transition from the ground state? (c) (5 points) What is the largest time I at which the perturbation of the ground state in this problem is still small enough to use first-order perturbation theory? ولا Pov