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

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.

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Correspondence to Mohammed Tayeb Meftah.

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Bekhouche, R., Meftah, M.T. & Korichi, Z. Comparative Study for N D-Dimensional Quantum Oscillators with Respect Fractional Derivative Senses. Few-Body Syst 58, 153 (2017). https://doi.org/10.1007/s00601-017-1315-1

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  • DOI: https://doi.org/10.1007/s00601-017-1315-1

Keywords

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