Few-Body Systems

, 58:153 | Cite as

Comparative Study for N D-Dimensional Quantum Oscillators with Respect Fractional Derivative Senses

  • Randa Bekhouche
  • Mohammed Tayeb Meftah
  • Zineb Korichi
Article

Abstract

In this paper, we focus our study on some systems in statistical mechanics based on the fractional quantum mechanics. At first, we present the partition function of a system composed of N independent fractional quantum oscillators in D-dimensional space. Secondly, based on the three fractional derivatives senses (Liouville, Reimann–Liouville, and Caputo), we calculate the partition function for each sense and we apply the result to 3-dimensional quantum oscillator. By this application, we have shown that the derivative senses, generally, lead to different partition functions.

Keywords

Fractional derivative Liouville Riemann–Liouville Caputo D-dimensional Quantum oscillator Partition function 

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Copyright information

© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  • Randa Bekhouche
    • 1
  • Mohammed Tayeb Meftah
    • 1
  • Zineb Korichi
    • 1
  1. 1.LRPPS Laboratory, Faculty of Mathematics and Matter SciencesUniversity of Kasdi MerbahOuarglaAlgeria

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