Bound-states for generalized trigonometric and hyperbolic Pöschl-Teller potentials

Abstract

We use the "tridiagonal representation approach" to solve the time-independent Schrödinger equation for the bound states of generalized versions of the trigonometric and hyperbolic Pöschl-Teller potentials. These new solvable potentials do not belong to the conventional class of exactly solvable problems. The solutions are finite series of square integrable functions written in terms of the Jacobi polynomial.

19 pages, 2 tables, 4 figures, typo "geometric" corrected as "trigonometric"

References in corpus (4)

• Tridiagonal Representation Approach in Quantum Mechanics
• Solution of an Open Problem about Two Families of Orthogonal Polynomials
• Deformed Morse-like potential
• Series solutions of Bessel-type differential equation in terms of orthogonal polynomials and physical applications

Cited by in corpus (1)

• Non-standard quantum algebras and infinite-dimensional PT-symmetric systems