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## Homework Statement

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?