Abstract
The density of states (DOS) of infinite quantum systems with continuous parts of the energy spectra represents a long-standing problem in quantum mechanics. The common definition of a DOS per unit energy and unit volume allows equilibrium statistical values of intensive physical quantities to be calculated. This DOS, however, disregards bound and quasibound states. Here we propose a DOS per unit energy and unit volume that also carries information on such states. The key elements of our approach are, first, the distinction between geometrical and dynamical spatial extensions of quantum states and second, the concept of states of equal quantum-mechanical weights. A set of formulas is provided that allows the DOS per unit energy and unit volume to be explicitly calculated for any infinite system. The general theory is illustrated by treating two examples, these being, first, an attracting one-dimensional δ potential and, second, a quantum well in a homogeneous electric field.
- Received 27 February 1990
DOI:https://doi.org/10.1103/PhysRevB.42.4708
©1990 American Physical Society