Regge Poles and Bound States of Nonrelativistic Scattering Systems

A heuristic argument which avoids using the Sommerfeld-Watson transform is presented for the existence of bound states for a potential at the poles of its partial-wave scattering amplitude in the physical sheet. We obtain a general formula for bound state Regge trajectories from the Jost function φ+(l, k2) and apply it to four potentials— Coulomb, harmonic oscillator, delta shell, and spherical well. The concluding section examines some properties of Regge trajectories in nonrelativistic scattering and the extension of Regge pole theory to relativistic particle interactions.