SEPARABLE QUASIPOTENTIAL FORMULATION OF RELATIVISTIC DYNAMICS FOR 3 POINT PARTICLES

In this paper I develop a relativistic Hamiltonian and Schrödinger equation for three particles using a generalization of the assumptions that give rise to Todorov's relativistic quasipotential equation for two particles. This formalism is treated by a method that leads to a generalization of the separable Lagrange equilateral-triangle solution from gravitational nonrelativistic to relativistic nongravitational bound-state problems in quantum as well as classical mechanics. As an example I derive an analytic solution for the spectrum of a three-body system bound by scalar Coulomb forces. © 1978 The American Physical Society.