Consider the following state of a harmonic oscillator at t = 0 written as a linear combi- nation of eigenstates of the number operator n|n) = nin), [ you may recall that the ladder operator a can be written 2h 2mhu (a) using the schrödinger equation, derive an expression for (t)) (b) calculate ()x(t) and ((t)x2(t) c) calculate < p > t-0 and show that it is a maximum when α . (d) calculate (0l(t) to derive an expression of the probability of being in the ground state as a function of time