Suppose the one-dimensional harmonic oscillator (mass m, frequency ω) is subjected to a...

Suppose the one-dimensional harmonic oscillator (mass m, frequency ω) is subjected to a driving force of the form , where f(t) is some specified function (I have factored out for notational convenience; f (t) has the dimensions of length). The Hamiltonian is

Assume that the force was first turned on at time . This system can be solved exactly both in classical mechanics and in quantum mechanics.2t

(a) Determine the classical position of the oscillator, assuming it started from rest at the origin Answer:

(b) Show that the solution to the (time-dependent) Schrodinger equation for this oscillator, assuming it started out in the nth state of the undriven oscillator is given by Equation 2.61), can be written as