For a harmonic oscillator in a state such that a measurement of energy would give either [itex]1/2\hbar\omega[/itex] or [itex]3/2\hbar\omega[/itex] with equal probabily. Write the wavefunction solution to the time-dependent Schrodinger equation.
2. The attempt at a solution
Given those energies I know [itex]\psi_0[/itex] and [itex]\psi_1[/itex] are the two states but I'm asked to chose the coefficients in front of them in the most general way, i.e. don't assume they are real. How do I do this?