Let ψn(x) be eigenfunctions of the Hamiltonian of the simple harmonic oscillator, with eigenvalues En. Assume that the wavefunction at the time t = 0 is given by Ψ(x, t = 0) = (1+i)/3 ψ0(x) + 2/3 ψ1(x) + 1/√3 ψ3(x).
a) What are the possible values of energy, if it is measured at t = 0?
b) Write down the probability of measuring each of the energies listed in part (a).
c) Write down an expression for the full time-dependent wavefunction, Ψ(x,t). Note: You are not required to write out explicit functional forms for the ψn(x).
