Semi-Relativistic Reflection and Transmission Coefficients for Two Spinless Particles Separated by a Rectangular-Shaped Potential Barrier

Abstract

A generalized Schrödinger approximation, due to Ikhdair & Sever, of the semi-relativistic two-body problem with a rectangular barrier in (1+1) dimensions is compared with exact computations. Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers. The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |ϵ − V0| < 2µc 2 , where µ is the reduced mass, ϵ the scattering energy, and V0 the barrier top energy. The approximate wave numbers are less accurate.

The semi-relativistic scattering states of the two-body spinless Salpeter equation with the Varshni potential model

“…These relativistic effects exist for a single Dirac mass in a potential model, described by Dirac Theory [8][9][10]. In the present study, we ignored the spin context and focus on the effects of twobody mass index on the scattering phase shift of the Varshni potential model.…”

Scattering states solutions of Klein–Gordon equation with three physically solvable potential models

“…With various methods, Klein-Gordon equation has been studied with some exactly solvable potentials [1][2][3][4][5][6][7][8][9]. The scattering state solutions of various potential models have been a subject of considerable interest in the recent year because it gives an insight to understand atomic structures, electronic configuration of atoms, resonance and many collisions process [9][10][11][12][13][14][15][16][17].…”

Relativistic Energies and Scattering Phase Shifts for the Fermionic Particles Scattered by Hyperbolical Potential with the Pseudo(spin) Symmetry

“…Scattering theory is very central to the study of several fields such as atomic, nuclear, high energy or condensed matter physics. It allows for descriptions and interpretations of many collisions processes such as excitation and ionization by particle or radiation impact [1][2][3][4][5][6][7]. Complete information about the quantum systems can only be obtained by investigating scattering state solutions of relativistic and nonrelativistic equations with quantum mechanical potential model.…”