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Thermodynamic quantities for the Klein–Gordon equation with a linear plus inverse-linear potential: Biconfluent Heun functions

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Abstract

We study some thermodynamics quantities for the Klein–Gordon equation with a linear plus inverse-linear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule from the biconfluent Heun’s equation. We use a method based on the Euler–MacLaurin formula to analytically compute the thermal functions by considering only the contribution of positive part of the spectrum to the partition function.

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Acknowledgements

One of authors (A A) is grateful to professor A. Fring from City University London and the Department of Mathematics for hospitality. This research was partially supported by the Scientific and Technical Research Council of Turkey and through a fund provided by University of Hacettepe.

The authors also thank the referee for comments which have improved the manuscript.

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Authors and Affiliations

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

    ALTUĞ ARDA

  2. Faculty of Engineering, Baskent University, Baglica Campus, Ankara, Turkey

    CEVDET TEZCAN

  3. Department of Physics, Middle East Technical University, 06531, Ankara, Turkey

    RAMAZAN SEVER

  4. Present address: Department of Mathematical Science, City University London, Northampton Square, London, EC1V 0HB, UK

    ALTUĞ ARDA

Authors
  1. ALTUĞ ARDA
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  2. CEVDET TEZCAN
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  3. RAMAZAN SEVER
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Correspondence to ALTUĞ ARDA.

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ARDA, A., TEZCAN, C. & SEVER, R. Thermodynamic quantities for the Klein–Gordon equation with a linear plus inverse-linear potential: Biconfluent Heun functions. Pramana - J Phys 88, 39 (2017). https://doi.org/10.1007/s12043-016-1347-y

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  • DOI: https://doi.org/10.1007/s12043-016-1347-y

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