Exact solutions of D-dimensional Klein–Gordon oscillator with Snyder–de Sitter algebra

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 state spectrum and the corresponding momentum space wave functions are obtained using Gegenbauer polynomials in the one-dimensional space and Jacobi polynomials in the D-dimensional 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 that 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 by Falek et al. [J. Math. Phys. 60, 013505 (2019)].