# Scattering states solutions of Klein-Gordon equation with three physically solvable potential models

## TL;DR

This paper derives scattering state solutions for the Klein-Gordon equation with three solvable potentials, analyzing phase shifts and bound states, and compares non-relativistic limits with existing literature.

## Contribution

It provides new analytical solutions for scattering states with Varshni, Hellmann, and Varshni-Shukla potentials for arbitrary angular momentum.

## Key findings

- Phase shifts depend on screening parameter, potential parameter, and angular momentum.
- Bound state energies agree with existing literature.
- Non-relativistic limits are consistent with known results.

## Abstract

The scattering state solutions of the Klein-Gordon equation with equal scalar and vector Varshni, Hellmann and Varshni-Shukla potentials for any arbitrary angular momentum quantum number l are investigated within the framework of the functional analytical method using a suitable approximation. The asymptotic wave functions, approximate scattering phase shifts, normalization constants and bound state energy equations were obtained. The non-relativistic limits of the scattering phase shifts and the bound states energy equations for the three potentials were also obtained. Our bound states energy equations are in excellent agreement with the available ones in the literature. Our numerical and graphical results indicate the dependence of phase shifts on the screening parameter \b{eta}, the potential parameter b and angular momentum quantum number l.

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Source: https://tomesphere.com/paper/1705.01577