Thermal properties of a two-dimensional Duffin-Kemmer-Petiau oscillator under an external magnetic field in the presence of a minimal length

Abstract

In this article, we investigate the solutions of a two-dimensional Duffin-Kemmer-Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) formalism of the Heisenberg generalized uncertainty principle. First, we obtain the eigensolutions in the ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of a ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions. We show that in the limit where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler-Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale. We conclude that in the literature there are several articles with the misleading thermal properties of the relativistic oscillators.