Relativistic equations with some point potentials

Abstract

Exact solutions have been obtained for relativistic one-dimensional integral equations that describe the scattering of two particles with potentials of the "delta function n-th derivative" type for n = 1, 2, 3. Based on the solutions, the transmission and reflection coefficients have been found and some their properties have been investigated.

Relativistic two-particle equations with superposition of delta-shell potentials: scattering and bound states

“…The solution of one-dimensional relativistic two-particle equations with the deltafunction potential and superposition of delta-function potentials was considered in [5,6]. These equations with potential "delta-function derivative of n-th order" δ (n) at n = 1, 2, 3 were solved in article [15]. The relativistic one-dimensional problem for nonlinear delta-function potential was considered in [16].…”

“…In this paper we consider the solution of relativistic partial two-particle equations for s-waves (9), (15) with the potential V 0 δ(r − a), which is localized on the sphere of finite radius a > 0 (in the three-dimensional case such potential is often called "delta-shell potential"), and with a superposition of two such potentials. The article is organized as follows.…”

“…Solutions of equations (15) for the superposition of the delta-shell potentials can be found by analogy with the scattering state case. The quantization conditions for the superposition of delta-shell potentials (25) are…”