An extended Levinson’s theorem

Abstract

We investigate the form Levinson’s theorem takes when the two-body scattering amplitude is not decomposed into partial waves. It is found that the theorem changes its structure in this case and is not merely the sum over angular momentum of the well-known partial wave results. The energy dependent quantity that replaces the partial wave phase shift turns out to be the trace of the two-body time delay operator. This extended version of the theorem remains valid for scattering by nonspherically symmetric potentials.