Answer Happy

one-dimensional harmonic oscillator V(x) = mw²r² is found in the following state A particle in a at time t = 0: 1 |v/(t = 0)) 510) + 1/ 11) + 1/1/12) where n) denotes the nth harmonic oscillator eigenstate. a) What is the expectation value of the energy at time t? b) What is the average value of the position at time t? c) Consider instead a harmonic oscillator in its ground state with a weak laser field applied after time t≥ 0, Vlaser (t) = ex sinnt, €<< mw²x. Use first-order time-dependent perturbation theory to show that the system cannot be found in any state higher than n = 1 at later times, and find the probability of finding the system in the first excited state, n = 1, at time t. Note that you should do any integrals but you need not simplify your expression mathematically.