PT symmetric form of the Hulthen potential

TL;DR

This paper introduces a new exactly solvable PT-symmetric complex potential based on a generalized Hulthen interaction, expanding the class of known potentials with real spectra and Jacobi polynomial solutions.

Contribution

It presents the fourth known example of an exactly solvable PT-symmetric complex potential with specific properties, extending previous models.

Findings

Identifies a new PT-symmetric complex potential in the Hulthen form.

Provides explicit solutions involving Jacobi polynomials.

Demonstrates the potential's real energy spectrum on a bent contour.

Abstract

The fourth, missing example of an exactly solvable complex potential with PT symmetry V(x) = [V(-x)]^* defined on a bent contour and leading, at the real energies, to the Jacobi polynomial wave functions is found in a generalized Hulthen interaction.