Pekeris-type approximation for the $l$-wave in a P\"oschl-Teller potential

TL;DR

This paper introduces a new approximation method for the centrifugal term in the radial equation of a particle in a P"oschl-Teller potential, enabling exact solutions for a broader class of potentials.

Contribution

It proposes a novel Pekeris-type approximation applicable to the most general P"oschl-Teller potential, improving upon existing methods.

Findings

Derived an approximate bound-state spectrum expression.

The approximation allows for exact solvability in more general cases.

Demonstrated the effectiveness of the new approximation.

Abstract

An approximation for the centrifugal term which transforms the radial equation for a particle in a P\"oschl-Teller potential into an exactly solvable approximate equation is proposed. In contrast to the approximations known in the literature, the new one can be used with the most general form of the central P\"oschl-Teller potential. An approximate expression for the bound-state spectrum is obtained.