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Time evolution of wavefunction of particle in a square well

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If you put

<psi|psi> = 1, you find:

A = 2 Squareroot[3/a^3]

To find the time evolution you can first expand psi> in energy eigenfunctions and then multiply each coefficient in that expansion by Exp[-i E_n t/h-bar] where E_n is the energy eigenvalue of the nth energy eigenfunction. To find the energy eigenfunctions note that the potential is symmetrical under a reflection about the point a/2. This symmetry relation translates into the fact that the energy eigenfunctions can be chosen to be eigenfunctions of the reflection operator. Since reflecting twice must yield the same function, the eigenvalue for reflection can be plus or minus one, so we are dealing with odd and even eigenfunctions. The function we want to expand is even under a reflection, so we only need to ...

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