Solutions of Schr\"odinger Equation with Generalized Inverted Hyperbolic Potential

TL;DR

This paper derives bound state solutions for the Schr"odinger equation with a generalized inverted hyperbolic potential, unifying several known potentials and providing explicit energy spectra and wave functions.

Contribution

It introduces a method to solve the Schr"odinger equation with a new generalized potential, encompassing known potentials as special cases.

Findings

Derived energy spectrum and wave functions for the generalized potential

Reduced results to Rosen-Morse, P"oschl-Teller, and Scarf potentials

Provided explicit formulas for special cases

Abstract

We present the bound state solutions of the Schr\"odinger equation with generalized inverted hyperbolic potential using the Nikiforov-Uvarov method. We obtain the energy spectrum and the wave function with this potential for arbitrary - state. We show that the results of this potential reduced to the standard known potentials - Rosen-Morse, Poschl - Teller and Scarf potential as special cases. We also discussed the energy equation and the wave function for these special cases.