- #1

cfwoods

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## Homework Statement

The equation [itex]\psi(x) = \frac{1}{sqrt(2)}\psi_0 (x) + \frac{i}{sqrt(5)}\psi_1 (x) + \gamma\psi_2 (x)[/itex]

is a combination of the first three eigenfunctions in the 1D harmonic oscillator. So, [itex]\psi_0 = Ae^{-mωx^2 /2\hbar}[/itex] and so on for the first and second excited states. If [itex]\psi_0[/itex], [itex]\psi_1[/itex] and [itex]\psi_2[/itex] are normalised, and [itex]\psi(x)[/itex] is also normalised, determine [itex]|\gamma|[/itex]

## The Attempt at a Solution

You can obtain the normalised functions for the ground state and first two excited states from a variety of methods, and you can then expand out [itex]\psi(x)[/itex]. I tried plugging that back into the time dependent Schrodinger equation, but that didn't help (and it also gave a messy derivative) so I am at a loss as to how i can proceed.