Bound-states for generalized trigonometric and hyperbolic Pöschl-Teller potentials
arXiv:2108.08978 · doi:10.1142/S0217751X22500129
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.
arXiv comment19 pages, 2 tables, 4 figures, typo "geometric" corrected as "trigonometric"
References in corpus (11)
- Complex Extension of Quantum Mechanics
- Solution of the nonrelativistic wave equation in the tridiagonal representation approach
- Quantum mechanics without potential function
- Tridiagonal Representation Approach in Quantum Mechanics
- Open problem in orthogonal polynomials
- Series solutions of Heun-type equation in terms of orthogonal polynomials
- Quantum mechanics with orthogonal polynomials
- Series solutions of Laguerre- and Jacobi-type differential equations in terms of orthogonal polynomials and physical applications
- 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