Thermodynamics Quantities for the Klein-Gordon Equation with a Linear plus Inverse-linear Potential: Biconfluent Heun functions

TL;DR

This paper analytically investigates thermodynamic properties of the Klein-Gordon equation with a combined linear and inverse-linear potential, utilizing biconfluent Heun functions and the Euler-MacLaurin formula for spectral and thermal analysis.

Contribution

It introduces an analytical method to compute thermodynamic quantities for a Klein-Gordon system with a complex potential using special functions and spectral quantization.

Findings

Derived energy eigenvalues using biconfluent Heun functions.

Computed thermal functions analytically considering positive spectrum.

Provided insights into the thermodynamics of relativistic quantum systems.

Abstract

We study some thermodynamics quantities for the Klein-Gordon equation with a linear plus inverse-linear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule coming from the biconfluent Heun's equation. We use a method based on the Euler-MacLaurin formula to compute the thermal functions analytically by considering only the contribution of positive part of spectrum to the partition function.