Eur. Phys. J. Plus (2016) 131: 323
https://doi.org/10.1140/epjp/i2016-16323-0

Regular Article

Schrödinger equation with a non-central potential: Some statistical quantities

¹ Department of Physics Education, Hacettepe University, 06800, Ankara, Turkey
² Faculty of Engineering, Baskent University, Baglica Campus, Ankara, Turkey
³ Department of Physics, Middle East Technical University, Ankara, Turkey

^* e-mail: arda@hacettepe.edu.tr

Received: 18 May 2016
Accepted: 19 August 2016
Published online: 20 September 2016

Abstract

In this paper, we study the dependence of some statistical quantities such as the free energy, the mean energy, the entropy, and the specific heat for the Schrödinger equation on the temperature, particularly in the case of a non-central potential. The basic point is to find the partition function which is obtained by a method based on the Euler-Maclaurin formula. At first, we present the analytical results supporting them with some plots for the thermal functions for one- and three-dimensional cases to find out the effect of the angular momentum. We also study then the effect of the angle-dependent part of the non-central potential. We discuss the results briefly for a phase transition for the system. We also present our results for a three-dimesional harmonic oscillator.