Generalized Levinson theorem for singular potentials in two dimensions - art. no. 012707

摘要

The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states N-m(b) in a given mth partial wave is related to the phase shift delta(m)(k) and the singularity strength of the potential. When the effective potential has an inverse square singularity at the origin of the form nu(2)/rho(2) and inverse square tail at infinity such as mu(2)/rho(2), Levinson's relation gives delta(m)(0)-delta(m)(infinity)=pi[N-m(b)+(u-mu)/2]. [References: 39]