# A statistical mechanical analysis on the bound state solution of an energy-dependent deformed Hulth\'en potential energy

## TL;DR

This paper analyzes the bound states of a Klein-Gordon particle in an energy-dependent deformed Hulthén potential across multiple dimensions, using statistical mechanics to explore thermodynamic properties.

## Contribution

It introduces a novel approach combining quantum bound state solutions with statistical mechanics for an energy-dependent deformed Hulthén potential.

## Key findings

- Energy spectra calculated in various limits and dimensions.
- Thermodynamic properties exhibit overlapping and distinct behaviors.
- Bound state solutions obtained via transcendental equations.

## Abstract

In this article, we investigate the bound state solution of the Klein Gordon equation under mixed vector and scalar coupling of an energy-dependent deformed Hulth\'en potential in D-dimensions. We obtain a transcendental equation after we impose the boundary conditions. We calculate energy spectra in four different limits and in arbitrary dimension via the Newton-Raphson method. Then, we use a statistical method, namely canonical partition function, and discuss the thermodynamic properties of the system in a comprehensive way. We find out that some of the thermodynamic properties overlap with each other, some of them do not.