What are the properties of a half infinite well and how do they affect the behavior of particles within it?

A half infinite well is a potential energy barrier that extends infinitely in one direction and has a finite depth. The properties of a half infinite well affect the behavior of particles within it by confining them to a limited region of space. This confinement leads to quantized energy levels and wave functions for the particles, which results in unique behavior such as particle reflection and transmission at the boundaries of the well.