IL NUOVO CIMENTO VOL. 107A, N. 8 Agosto 1994 On a Novel Relativistic Quasi-Potential Equation for Two Scalar Particles (*). A. B. ARBUZOV Laboratory of Theoretical Physics, Joint Institute for Nuclear Research Dubna, Head Post Office P.O. Box 79, 101000 Moscow, Russia (ricevuto il 13 Dicembre 1993; approvato il 24 Gennaio 1994) Summary. -- A novel quasi-potential relativistic equation for two scalar particles of arbitrary masses is presented. The derivation is demonstrated in detail. For the electromagnetic interaction, the equation has the form of the one-particle SchrSdinger equation. The interaction is introduced by the minimal substitution. The exact solutions are considered in several limits: non-relativistic, equal masses, one particle at rest and ultrarelativistic. The problem of interaction retardation is discussed. PACS 12.90 - Miscellaneous theoretical ideas and models. PACS 11.10.Qr - Relativistic wave equations. 1. - Introduction. The present work deals with the old problem of a relativistic description of two interacting particles. The quasi-potential approach is presumably the most popular one among others. This approach to the two-particle relativistic problem has been developed first by Logunov and Tavkhelidze[1]. Quasi-potential equations are differential ones with the structure of a one-body equation, with an energy- dependent quasi-potential. In most applications, they are considered for stationary states in the centre-of-mass (CM) system. The most popular solution of the two-body spinless problem is given by the Todorov-Komar-Droz-Vincent equation[2-4]. Similar equations, for the two-fermion and fermion-boson cases, have been proposed by Sazdjian [5]. In modern works [6-7] the authors consider the Todorov equation as the base one has to compare with. Our approach differs from that of Logunov and Tavkhelidze. It is based on the principle of correspondence to the Schr6dinger equation for two particles. We shall work in the frame of the relativistic quantum mechanics (RQM). We take as the (*) The author of this paper has agreed to not receive the proofs for correction. 1263