Relativistic two-particle one-dimensional scattering problem for superposition of delta-potentials

On the solution of the relativistic quasipotential equation for the superposition of a local potential and of the sum of nonlocal separable quasipotentials

“…Actually, the function (0) 1 ( ) l V χ defined by relations (12) and (13) is everywhere continuous, and the function…”

“…The quasipotential approach [8] is still an efficient method of relativistic description of two-particle systems [9][10][11][12]. In the present work, the solution of a finite-difference quasipotential equation is investigated in the context of the relativistic quasipotential approach to quantum field theory [13].…”

Relativistic equations with some point potentials

“…Solutions of equation (1) with potential 0 ( ) ( ) V V ρ = δ ρ and with superpositions of potentials of this type are given elsewhere [7,8]. In this paper, we present the solutions of equation (1) with potentials of the form…”

“…To find exact solutions of this type of integral equations is a challenge; however, this problem can be solved for some potentials, for instance, by the generalized Frobenius method [6]. For the potentials that are superpositions of Dirac delta functions, these solutions [7,8] are similar to the corresponding nonrelativistic ones.…”

“…The relativistic generalization of the one-dimensional integral equation for a wave function (for the state of scattering of two particles) is an equation of the form [7] …”