Levinson's theorem in a semiconductor quantum well

Abstract

The relation between the phase shift of zero energy continuous spectrum wavefunctions and the number of bound states in a symmetric semiconductor quantum well is discussed. In the case of nonuniform effective mass, Levinson's theorem is shown to be valid in its usual form. However, in the high-energy range the phase shift tends to infinity, oscillating about a straight line, very different from the case of constant effective mass, where it tends to zero. Numerical calculations are given for a rectangular quantum well.