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Theoretical and Mathematical Physics

Quasipotential formalism for a system of two particles with spins 0 and 1/2

V.R. Garsevanishvili, S. V. Goloskokov, V. Matveev, L.A. Slepchenko

Published Sep 1, 1972• 4 citations
Publisher
DOI
10.1007/bf01035608

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In this paper I develop a relativistic Hamiltonian and Schr\"odinger 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.