Confined Particles

Confinement of a wave to a limited spatial region results in rather peculiar behavior -- the wave can only fit comfortably into the confined region if the wave frequency, and hence the associated particle energy, takes on a limited set of possible values. This is the origin of the famous quantization of energy, from which the ``quantum'' in quantum mechanics comes. We will explore two types of confinement, position confinement due to a potential energy well, and rotational confinement due to the fact that rotation of an object through $2 \pi \mbox{ radians}$ returns the object to its original orientation.