A Lorentz covariant representation of bound state wave functions

Abstract

We present a method enabling us to write in relativistic manner the wave function of some particular two particle bound state models in quantum mechanics. The idea is to expand the bound state wave function in terms of free states and to introduce the potential energy of the bound system by mens of the 4-momentum of an additional constituent, supposed to represent in a global way some hidden degrees of freedom. The procedure is applied to the solutions of the Dirac equation with confining potentials which are used to describe the quark antiquark bound states representing a given meson state.