The equivalent potential for relativistic confined systems

Abstract

In previous papers a method of obtaining bound states and wavefunctions for confined relativistic systems was presented. The input is the asymptotic expansion of the two-point functions. Confinement is imposed by systematic removal of the two-particle cut. We extend this method by developing an equivalent (angular momentum dependent) potential, which gives the correct wavefunction to a given order of R, the infrared scale parameter. We prove the uniqueness of the wavefunction by requiring that there are no CDD poles and by the connection of our moment conditions to the requirement that the residues of the bound-state poles must be positive. Finally we test the bound-state approximation for a system defined by an equivalent potential V(r) = λ 2 tanh 2( g 2r λ ) . Although in this case there is a threshold we still find excellent results when λ 2 g 2 is large, i.c., when there are many bound states.