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Relativistic thermostatistical analysis for a combined potential within spatially dependent mass scheme

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Abstract

We study some thermodynamical quantities solving the Klein–Gordon equation by using a potential combining Coulomb, and Woods-Saxon potentials for a particular spatially dependent mass form. We find the energy eigenvalues, and the corresponding wave functions approximately by reforming the Klein–Gordon equation similar to a Riemann-type equation whose solutions are given in terms of hypergeometric function \(\,_2F_1(p', q'; r'; z)\). After obtaining them analytically, we get the partition function which is based on studying the thermostatistical quantities such as specific heat and Tsallis entropy. As a function of temperature, the specific heat shows a maximum structure which is the well-known Schottky anomaly at very low temperature. Tsallis entropy enhances with increasing the temperature for different surface thickness and width of the potential.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Author’s comment: This is a theoretical study and no experimental data.]

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Authors and Affiliations

  1. Division of Physics Education, Hacettepe University, 06800, Ankara, Turkey

    Altuğ Arda

  2. Department of Physics, Jahrom University, 74135-111, Jahrom, Iran

    Hamid-Reza Rastegar Sedehi

  3. Department of Physics, Middle East Technical University, 06800, Ankara, Turkey

    Ramazan Sever

Authors
  1. Altuğ Arda
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  2. Hamid-Reza Rastegar Sedehi
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  3. Ramazan Sever
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Correspondence to Hamid-Reza Rastegar Sedehi.

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Arda, A., Sedehi, HR.R. & Sever, R. Relativistic thermostatistical analysis for a combined potential within spatially dependent mass scheme. Eur. Phys. J. Plus 137, 452 (2022). https://doi.org/10.1140/epjp/s13360-022-02632-8

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