Particle in a square well

Craig made several interesting points in this quote from an interview at the end of the semester. The first was that the particle-in-a-box was not a good example because it wasn t useful as Craig pointed out, it is unlikely that he would ever deal with the particular case of a one-dimensional particle in a square well. Second, and even more intriguing, Craig commented that although he understood that the particle-in-a-box was an example, it was not the one he needed to see. 

Imagine that a particle of mass m is free to move along the x axis between x = 0 and x = L, with no change in potential (set F = 0 for 0 < x < L). At x = 0 and L and at all points heyond these limits the particle encounters an infinitely repulsive barrier (V = oo for X <0, X > L). The situation is illustrated in Fig. 2-1. Because of the shape of this potential, this problem is often referred to as a particle in a square well or a particle in a box problem. It is well to bear in mind, however, that the situation is really like that of a particle confined to movement along a finite length of wire. 

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