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We use the Tridiagonal Representation Approach (TRA) to obtain exactscattering and bound states solutions of the Schr\"odinger equation forshort-range inverse-square singular hyperbolic potentials. The solutions areseries of square integrable functions written in terms of the Jacobi polynomialwith the Wilson polynomial as expansion coefficients. The series is finite forthe discrete bound states and infinite, but bounded, for the continuumscattering states.

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