Skip to main content
SpringerLink
Log in

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

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Kibler, T. Negadi, Int. J. Quantum Chem. 26, 405 (1984)

    Article  Google Scholar 

  2. Z.M. Cang, W.Z. Bang, Chin. Phys. 16, 1863 (2007)

    Article  ADS  Google Scholar 

  3. J.L. Katz, A. Misra, P. Spencer, Y. Wang, S. Bumrerraj, T. Nomurrad, S. Eppell, M. Tabib-Azar, Mater. Sci. Eng. C 27, 450 (2007)

    Article  Google Scholar 

  4. H. Hermann, Phys. Status Solidi B 104, k39 (1980)

    Article  ADS  Google Scholar 

  5. L. Monette, M.P. Anderson, Model. Simul. Mater. Sci. Eng. 2, 53 (1994)

    Article  ADS  Google Scholar 

  6. A.A. Makarov, J.A. Smorodinsky, K. Valiev, P. Winternitz, Nuovo Cimento A 52, 1061 (1967)

    Article  ADS  Google Scholar 

  7. H. Hartmann, Theor. Chim. Acta 24, 201 (1972)

    Article  Google Scholar 

  8. B. Gonul, I. Zorba, Phys. Lett. A 269, 83 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  9. A.D. Alhaidari, J. Phys. A 38, 3409 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  10. G.A. Kerimov, J. Phys. A 39, 1183 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  11. G.A. Kerimov, Phys. Lett. A 358, 176 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  12. A. Khare, R.K. Bhaduri, Am. J. Phys. 62, 1008 (2010)

    Article  ADS  Google Scholar 

  13. A. de Souza Dutra, M. Hott, Phys. Lett. A 356, 215 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  14. M. Chabab, A. El Batoul, M. Oulne, J. Math. Phys. 56, 062111 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  15. M. Hamzavi, A.A. Rajabi, Eur. Phys. J. Plus 128, 29 (2013)

    Article  Google Scholar 

  16. M.H. Pacheco, R.R. Landim, C.A.S. Almeida, Phys. Lett. A 311, 93 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  17. M.H. Pacheco, R.V. Maluf, C.A.S. Almeida, R.R. Landim, EPL 108, 10005 (2014)

    Article  ADS  Google Scholar 

  18. A. Boumali, Elect. J. Theor. Phys. 12, 1 (2015)

    Google Scholar 

  19. V. Santos, R.V. Maluf, C.A.S. Almeida, Ann. Phys. 349, 402 (2014)

    Article  ADS  Google Scholar 

  20. A. Boumali, H. Hassanabadi, Eur. Phys. J. Plus 128, 124 (2013)

    Article  Google Scholar 

  21. H. Hassanabadi, S. Sargolzaeipor, B.H. Yazarloo, Few-Body Syst. 56, 115 (2015)

    Article  ADS  Google Scholar 

  22. S. Hassanabadi, M. Ghominejad, Adv. High Energy Phys. 2014, 185169 (2014)

    Google Scholar 

  23. A. Boumali, Phys. Scr. 76, 669 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  24. S.H. Dong, M. Lozada-Cassou, J. Yu, F. Gimenez-Angeles, A.L. Rivera, Int. J. Quantum Chem. 107, 366 (2007)

    Article  ADS  Google Scholar 

  25. C. Tezcan, R. Sever, Int. J. Theor. Phys. 48, 337 (2009)

    Article  MathSciNet  Google Scholar 

  26. F. Cooper, A. Khare, U.P. Sukhatme, Phys. Rep. 251, 267 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  27. M. Abramowitz, I.A. Stegun (Editors), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, New York, 1965)

  28. A. Tari, The Specific Heat of Matter at Low Temperatures (Imperial College Press, London, 2003)

Download references

Author information

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, Ankara, Turkey

    Ramazan Sever

Authors
  1. Altuğ Arda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cevdet Tezcan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ramazan Sever
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Altuğ Arda.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arda, A., Tezcan, C. & Sever, R. Schrödinger equation with a non-central potential: Some statistical quantities. Eur. Phys. J. Plus 131, 323 (2016). https://doi.org/10.1140/epjp/i2016-16323-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2016-16323-0

Search

Navigation