Aparticle of mass m in a 1d harmonic oscillator with frequency w, at time t = 0 is in a linear superposition of the ground and the first excited eigenstates, specifically, it has wave function 14(x,0)) - a[14) +expliq) 4.)]. (a) normalize the wave function. (b) find the coefficients cn in the series expansion 144(x,1)) - cm14(x)) exp[-i e,1/ħ]. if the energy is measured at time t, what are the possible values and what are the probabilities? find the expectation value of the hamiltonian ((x, t)|h1 4(x, t)) in this state. (c) find the expectation value of the momentum of the particle at time t, (4(x, t) p14(x, (d) find the value of the phase q such that (p) reaches its maximum value at time t=0. hint: you can take derivatives, or you can use eq. 2.69: =iħmo/2câ. - â