Harmonic oscillator (25 marks): consider a linear harmonic oscillator with the solution de- fined by the ladder operators a and a defined in class. use the number basis in) to do the following. class. use the nuim such that (ψ x1) is as large as a) construct a linear combination of 10) and 11) to form a state l possible. b) suppose that the oscillator is in the state constructed in a) at time t = 0, write an expression to de- scribe the time dependence of this state state for t > 0. evaluate the expectation value (t) x r(t)) as a function of time for t > 0. c) defining (δ2p = (t)lx? it((t)x1r(t))2. calculate (ar)2