Trapping Particles in Square Well Potentials: Wave Functions
One of the most fundamental problems of quantum physics deals with particles trapped on a submicroscopic level in a square well. The square well is always a favorite problem in quantum mechanics classes because the wave function works out so nicely.
The square well has many variations — you can have square wells that are symmetric around the origin, that have infinite walls, that have finite walls, and more. Here’s the square well at its most basic:
This is a one-dimensional well, so you’re concerned only with the x direction; therefore, the Schrödinger equation looks like this:
The wave function looks like this:
where A and B are constants.