Q-deformed superstatistics of the anharmonic oscillator for unrelativistic and relativistic (K–G equation) cases in noncommutative plane

Abstract

In this article, we present the thermodynamical properties of the anharmonic oscillator for unrelativistic and relativistic K–G equations in the presence of an external magnetic field in noncommutative plane using q-deformed superstatistics. The explicit form of energy eigenvalues and the wave functions of the considered system are derived in terms of the bi-confluent Heun functions. Subsequently, by employing the effective Boltzmann factor, the thermodynamical properties of the anharmonic oscillator ensemble for both cases are obtained and, some graphs are plotted for the clarity of our results.