Rules of wavefunctions in QM

1. The problem statement, all variables and given/known data

[PLAIN] [Broken]

2. Relevant equations

3. The attempt at a solution

My question is what do I need to prove to show that the wave function is acceptable. So far all I can think of is showing that the wave function is 0 outside the boundaries (infinite square well) and that the equation can be normalized. [tex]\int |\Psi(x,t)|^2dx=1[/tex]
Am I missing any postulates? Also, if someone could give me an example of how a wave function isn't spatial it would help a lot.
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As long as the wave function is a member of Hilbert Space, the wave function is acceptable. So in this case, continuous and normalizable is okay.

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