New conditionally exactly solvable potentials of exponential type

Abstract

Based on a method that produces the solutions to the Schrodinger equations of partner potentials, we give two conditionally exactly solvable partner potentials of exponential type defined on the half line. These potentials are multiplicative shape invariant and each of their linearly independent solution includes a sum of two hypergeometric functions. Furthermore we calculate the scattering amplitudes and study some of their properties.

16 pages, 5 figures

References in corpus (2)

• A conditionally exactly solvable generalization of the inverse square root potential
• A conditionally exactly solvable generalization of the potential step

Cited by in corpus (4)

• Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity
• A new exactly integrable hypergeometric potential for the Schrödinger equation
• A Schrödinger potential involving $x^{\frac{2}{3}}$ and centrifugal-barrier terms conditionally integrable in terms of the confluent hypergeometric functions
• The third five-parametric hypergeometric quantum-mechanical potential