Superstatistics of the Dunkl oscillator

Abstract

We use the momentum operator with the Dunkl derivative in quantum mechanics and derive its Schrodinger equation in one dimension with a harmonic oscillator potential. With the energy eigenvalues of such systems, we calculate their principal thermodynamical properties, the Helmholtz free energy, mean energy and entropy, and discuss the effects of the Dunkl parameter and modified Dirac delta function parameters on thermodynamical quantities. Then we use the superstatistics and calculate the thermodynamical properties of the system and analyze the effects of all the parameters on the thermodynamical quantities. We reduce all the results to the limit case of ordinary statistical mechanics. (C) 2021 Elsevier B.V. All rights reserved.