Learning Goal: To understand the qualities of the finite square-well potential and how to connect solutions to the Schrödinger equation from different regions. The case of a particle in an infinite potential well, also known as the particle in a box, is one of the simplest in quantum mechanics. The closely related finite potential well is substantially more complicated to solve, but it also shows more of the qualities that are characteristic of quantum systems. The potential energy function for a finite square-well potential is