Materials exam study help/Request for 3 to 5 potential well problems worked out.

I have an exam tomorrow in my materials and devices class and am trying get more experience working potential well problems.

The text for the class is Neamen - Semiconductor Physics and devices.

I'd like to get 3 to 5 worked out problems involving the use of schroedinger's equation (position dependant - not involving time) and boundary conditions to specify wave functions in a potential well with potential barriers of differing values.  Short descriptions of why something was done on a step would be nice.

I'd like to study the examples and then try to work them own my own.

A couple of other things...

Is there any easy way to find out the distance to the nearest neighbors in a cubic structure? (i.e. zinc blende, face centered...)  The geometry is not always clear to me.

I don't understand Density of States for energy distributions very well.  Are there some core ideas here?  How are Density of States and Energy related?  What is meant by K space?  What kind of problems could be asked regarding effective mass of electrons and holds?  Are there simple formulas to calculate these values?

Thank you.