Proving Acceptable Wave Functions in Quantum Mechanics

[xago]

Homework Statement

[PLAIN]http://img716.imageshack.us/img716/8330/werhc.png

Homework Equations

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. $$\int |\Psi(x,t)|^2dx=1$$
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.

 

[Mindscrape]

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.