Can anyone give me a really simple example on how to use the eqn above to solve it?
Using the Schrodinger equation is simply an application of differential equations:
You've done the one-dimensional "particle in a box" a.k.a. "infinite square well", right? Try the three-dimensional "rectangular" version in Cartesian coordinates. A Google search for things like "three dimensional square well" or "schrodinger equation three dimensional box" should find lecture notes about it. Maybe include the word "rectangular."
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