Classical limit and generalizations of the homogeneous quasipotential equation for scalar interactions

Abstract

The classical limit of Todorov's relativistic Schrödinger equation for scalar interactions is presented in a Hamiltonian context. The consequences of limitations on the coupling-constant size that exist in this quantum equation for bound states appear as orbital limitations in the classical case. A systematic method of generalizing the classical equations which removes these orbital restrictions is developed. The corresponding quantum equations do not display any limitations on the coupling-constant size. An exactly soluble example is given that displays very deep binding. In this example the total center-of-mass energy of two equal-mass bound particles goes to zero as the coupling constant goes to infinity.