1. Consider a simple one-dimensional harmonic oscillator and assuming that at time t = 0 the state of the system is given by the wave function 4 Tab(0)) = V50 p0(x) + (2) + 50 02(x) V50 where is understood by on (x) the autofunction corresponding to the n - th excited state of the oscillator harmonic. for (a) Find the wave function |(t)) for t> 0. (b) Find the mean value of the energy for t> 0. (c) Obtain the mean value of the impulse as a function of time (p(t). (d) Calculate the probability of finding the system in the initial state in an instant t > 0.