Square Well Bound States

One can determine the nature and energy of bound state wave functions for a square well by using the wave equation and matching conditions, continuity and smoothness, at the boundaries. This video shows how to do that for a single finite square well. Notice that in the context of finding the wave function parameters and energy, one determines two parameters related to length scales. One is k, which is related to the wavelength of the electron wave function inside the well. The other is q. q is a very important parameter because it tells you how gradually the evanescent part of the electron wave decays outside the well. 1/q is a length scale which tells you how far the evanescent part of the electron wave function extends outside the well. This is important when one is thinking of putting wells next to each other. This length scale helps determine what we mean by close and far.