Exact scattering and bound states solutions for novel hyperbolic potentials with inverse square singularity

Abstract

We use the Tridiagonal Representation Approach (TRA) to obtain exact scattering and bound states solutions of the Schrödinger equation for short-range inverse-square singular hyperbolic potentials. The solutions are series of square integrable functions written in terms of the Jacobi polynomial with the Wilson polynomial as expansion coefficients. The series is finite for the discrete bound states and infinite, but bounded, for the continuum scattering states.

11 pages, 1 table, 1 figure

References in corpus (3)

• Solution of the nonrelativistic wave equation in the tridiagonal representation approach
• The Wilson-Racah Quantum System
• Exact solvability of two new 3D and 1D nonrelativistic potentials within the TRA framework