The Schrödinger equation is considered for the case of a (charged) particle which is rigidly restricted to a finite region within which it is subject to a linear (electric) potential. Expressions are obtained for the energy and polarization of the quantum levels in the case where the field is small. Exact values for these properties in a stronger field are calculated for a few representative cases.

The properties of a canonical assembly of such systems are treated. In particular, the polarization of such an assembly is determined as a function of temperature.

• Received 11 August 1953

DOI:https://doi.org/10.1103/PhysRev.94.292