Construction of potential functions associated with a given energy spectrum — An inverse problem II

We continue our solution of the inverse problem started by the first author in [Int. J. Mod. Phys. A 35, 2050104 (2020)]. Additional potential functions for exactly solvable problems that correspond to the same energy spectrum formula but for different energy polynomials and bases are found. In this work, we obtain a class of potential functions associated with the Wilson polynomial and “Jacobi basis.”

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

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.