Exact Solutions of D-dimensional Klein-Gordon Oscillator with Snyder-de Sitter Algebra

TL;DR

This paper analytically solves the Klein-Gordon oscillator in D-dimensional Snyder-de Sitter space, revealing how quantum algebra modifications affect the spectrum, wave functions, and thermodynamic properties of relativistic bosons.

Contribution

It provides exact solutions for the Klein-Gordon oscillator in arbitrary dimensions under Snyder-de Sitter algebra, extending previous two-dimensional analyses.

Findings

Exact bound state spectrum obtained using special polynomials.

Thermodynamic corrections increase free energy, decrease entropy and specific heat.

Extended understanding of relativistic bosons in quantum algebra-modified spacetime.

Abstract

We study the effects of Snyder-de Sitter commutation relations on relativistic bosons by solving analytically in the momentum space representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and the corresponding momentum space wave functions are obtained using Gegenbauer polynomials in one dimension space and Jacobi polynomials in D dimensions case. Finally, we study the thermodynamic properties of the system in the high temperature regime where we found that the corrections increase the free energy but decrease the energy, the entropy and the specific heat which is no longer constant. This work extends the part concerning the Klein-Gordon oscillator for the Snyder-de Sitter case studied in two-dimensional space in J. Math. Phys. 60, 013505 (2019).