Cohesive energy for a square well potential 

(a) Find an expression for the binding energy of an electron in one dimension in a single square well of depth U₀ and width a. (This Is the standard first problem m elementary quantum mechanic) Assume that the solution is symmetric about the midpoint of the well.

(b) Find a numerical result for the binding energy in terms of U₀ for the special case |U₀| =2h² /ma² and compare with the appropriate limit of Fig. 20. In this limit of widely separated wells the band width goes to zero, so the energy for k = 0 is the same as the energy for other k in the lowest energy band. Other bands are formed from lime excited states of the well, in this limit