Bound-state solutions of the Schrödinger equation for two novel potentials

Abstract

We solve the one-dimensional Schrödinger equation for the bound states of two potential models with a rich structure as shown by their "spectral phase diagram". These potentials do not belong to the well-known class of exactly solvable problems. The solutions are finite series of square integrable functions written in terms of the Jacobi polynomials.

arXiv comment16 pages, 2 tables, 4 figures. arXiv admin note: text overlap with arXiv:2108.08978

References in corpus (7)

• Bound States in one and two Spatial Dimensions
• Solution of the nonrelativistic wave equation in the tridiagonal representation approach
• Tridiagonal Representation Approach in Quantum Mechanics
• Open problem in orthogonal polynomials
• Solution of an Open Problem about Two Families of Orthogonal Polynomials
• Deformed Morse-like potential
• Construction of potential functions associated with a given energy spectrum -- An inverse problem. II