Levinson’s Theorem and the Nonlocal Saito Potential

Abstract

We consider Levinson's theorem for the nonlocal Saito potential. We find that the phase of the Jost function gives a correct result for the zero-energy phase shift of π associated with the additional node in the scattering wavefunction. This analysis takes into account the zero-energy continuum bound state of the potential. A comparison is given with previous results which do not consider the possibility that such a state is present.