Schrödinger models for solutions of the Bethe–Salpeter equation in Minkowski space

Abstract

By application of the ``geometric spectral inversion'' technique, which we have recently generalized to accommodate also singular interaction potentials, we construct from spectral data emerging from the solution of the Minkowski-space formulation of the homogeneous Bethe--Salpeter equation describing bound states of two spinless particles a Schr\"odinger approach to such states in terms of nonrelativistic potential models. This spectrally equivalent modeling of bound states yields their qualitative features (masses, form factors, etc.) without having to deal with the more involved Bethe--Salpeter formalism.