Skip to main content
SpringerLink
Log in

Study of a 2D charged particle confined by a magnetic and AB flux fields under the radial scalar power potential

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

Abstract.

We present a more general form of the Schrödinger equation in curved space by introducing the magnetic fields. Further, we solve the non-relativistic wave equation with the radial scalar power potential (RSPP) under the influence of magnetic and Aharonov-Bohm (AB) flux fields by using the curvilinear coordinates system in such space. With this requirement, the energy spectrum and the corresponding wave functions have been calculated by means of the series method. Our analytical results are compared with other results and found to be in a good agreement. Furthermore, the main thermodynamic functions, such as the free energy, the mean energy, the entropy, the specific heat, the persistent currents and the magnetization, have been calculated by using the characteristic function. Some plots of the numerical results of the thermodynamic quantities are shown. Finally, we discuss our results.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Flugge, Practical Quantum Mechanics (Springer-Verlag, Berlin, Heidelberg, New York, 1974)

  2. S.H. Dong, M. Lozada-Cassou, Phys. Lett. A 330, 168 (2004)

    Article  ADS  Google Scholar 

  3. M.C. Zhang, G.H. Sun, S.H. Dong, Phys. Lett. A 374, 704 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  4. C.S. Jia, Y. Li, Y. Sun, L.T. Sun, Phys. Lett. A 311, 115 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  5. L.Z. Yi, Y.F. Diao, J.Y. Liu, C.S. Jia, Phys. Lett. A 333, 212 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  6. O. Aydogdu, R. Sever, Ann. Phys. (NY) 325, 373 (2010)

    Article  ADS  Google Scholar 

  7. G. Chen, Phys. Lett. A 326, 55 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  8. A. Arda, R. Sever, Commun. Theor. Phys. 58, 27 (2012)

    Article  ADS  Google Scholar 

  9. S. Ortakaya, Chin. Phys. B 21, 070303 (2012)

    Article  Google Scholar 

  10. A. Ishkhanyan, EPL 115, 20002 (2016)

    Article  ADS  Google Scholar 

  11. M. Eshghi, H. Mehraban, S.M. Ikhdair, Acta Math. Appl. Sin. 31, 1131 (2015)

    Article  Google Scholar 

  12. M. Eshghi, H. Mehraban, J. Kor. Phys. Soc. 67, 1118 (2015)

    Article  ADS  Google Scholar 

  13. M. Eshghi, H. Mehraban, Chin. J. Phys. 50, 533 (2012)

    Google Scholar 

  14. M. Eshghi, H. Mehraban, J. Math. Phys. 57, 082105 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  15. M. Eshghi, H. Mehraban, C. R. Phys. 18, 47 (2017)

    Article  ADS  Google Scholar 

  16. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  17. S.V. Kryuchkov, E.I. Kukhar, Phys. B 445, 93 (2014)

    Article  ADS  Google Scholar 

  18. C. Weishbuch, B. Vinter, Quantum Semiconductor Heterostructure (Academic Press, New-York, 1993)

  19. C. Frankenberg, J.F. Meiring, M. Van Weele, U. Platt, T. Wagner, Science 308, 1010 (2005)

    Article  ADS  Google Scholar 

  20. A. Baura, M. Kumar Sen, B. Chandra Bag, Chem. Phys. 417, 30 (2013)

    Article  ADS  Google Scholar 

  21. H. Haken, H.C. Wolf, Molecular Physics and Elements of Quantum Chemistry: Introduction to Experiments and Theory (Springer, Berlin, 1995)

  22. A. Arda, R. Sever, J. Math. Chem. 50, 971 (2012)

    Article  MathSciNet  Google Scholar 

  23. E.R. Figueiredo Medeiros, E.R. Bezerra de Mello, Eur. Phys. J. C 72, 2051 (2012)

    Article  ADS  Google Scholar 

  24. Al.L. Efros, A.L. Efros, Sov. Phys. Semicond. 16, 772 (1982)

    Google Scholar 

  25. X. Yao, A. Belyanin, J. Phys.: Condens. Matter. 25, 054203 (2013)

    ADS  Google Scholar 

  26. R. Khordad, Phys. B 406, 620 (2011)

    Article  ADS  Google Scholar 

  27. Vl.A. Margulis, E.E. Muryumin, E.A. Gaiduk, J. Opt. 16, 125203 (2014)

    Article  ADS  Google Scholar 

  28. W. Xie, S. Liang, Phys. B 406, 4657 (2011)

    Article  ADS  Google Scholar 

  29. R. Sever, C. Tezcan, M. Aktas, O. Yesiltas, J. Math. Chem. 43, 845 (2008)

    Article  MathSciNet  Google Scholar 

  30. V.A. Harutyunyan, E.M. Kazaryan, H.A. Kostanyan, H.A. Sarkisyan, Phys. E 36, 114 (2007)

    Article  Google Scholar 

  31. B.J. Falaye, G.-H. Sun, R. Silva-Ortigoza, S.H. Dong, Phys. Rev. E 93, 053201 (2016)

    Article  ADS  Google Scholar 

  32. N. Raigoza, A.L. Morales, C.A. Duque, Phys. B 363, 262 (2005)

    Article  ADS  Google Scholar 

  33. Y. Naim, J. Vahedi, R. Soltani, Opt. Quantum Electron. 47, 2947 (2015)

    Article  Google Scholar 

  34. M.S. Atoyan, E.M. Kazaryan, H.A. Sarkisyan, Physica E 22, 860 (2004)

    Article  ADS  Google Scholar 

  35. L.A. Falkovsky, J. Phys.: Conf. Ser. 129, 012004 (2008)

    Google Scholar 

  36. A. Ghoshal, Y.K. Ho, Phys. Rev. E 81, 016403 (2010)

    Article  ADS  Google Scholar 

  37. M.L. Glasser, N.H. March, L.M. Nieto, Phys. Lett. A 376, 1477 (2012)

    Article  ADS  Google Scholar 

  38. S.M. Ikhdair, B.J. Falaye, Chem. Phys. 421, 84 (2013)

    Article  ADS  Google Scholar 

  39. V. Santos, R.V. Maluf, C.A.S. Almeida, arXiv:1401.8051v2 (2014)

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

    Google Scholar 

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

    Article  Google Scholar 

  42. M.S. Reis, S. Soriano, Appl. Phys. Lett. 102, 112903 (2013)

    Article  ADS  Google Scholar 

  43. A. Boumali, Phys. Scr. 90, 045702 (2015)

    Article  ADS  Google Scholar 

  44. S.-H. Dong, M. Lozada-Cassou, J. Yu, F. Jiménez-Ángeles, A.L. Rivera, Int. J. Quantum Chem. 102, 366 (2007)

    Article  ADS  Google Scholar 

  45. S.-H. Dong, M. Cruz-Irisson, J. Math. Chem. 50, 881 (2012)

    Article  MathSciNet  Google Scholar 

  46. C.-S. Jia, L.-H. Zhang, C.-W. Wang, Chem. Phys. Lett. 667, 211 (2017)

    Article  ADS  Google Scholar 

  47. I.C. Fonseca, K. Bakke, Proc. R. Soc. A 471, 20150362 (2015)

    Article  ADS  Google Scholar 

  48. A.B. Oliveira, K. Bakke, Proc. R. Soc. A 472, 20150858 (2016)

    Article  ADS  Google Scholar 

  49. K. Bakke, Ann. Phys. 241, 86 (2014)

    Article  ADS  Google Scholar 

  50. L.L. Vitoria, K. Bakke, Eur. Phys. J. Plus 131, 36 (2016)

    Article  Google Scholar 

  51. L.L. Vitoria, C. Furtado, K. Bakke, Ann. Phys. 370, 128 (2016)

    Article  ADS  Google Scholar 

  52. A. Ronveaux, Heun's Differential Equations (Oxford University Press, Oxford, 1995)

  53. M. Eshghi, H. Mehraban, S.M. Ikhdair, Eur. Phys. J. A 52, 201 (2016)

    Article  ADS  Google Scholar 

  54. S.M. Ikhdair, B.J. Falaye, M. Hamzavi, Ann. Phys. 353, 282 (2015)

    Article  ADS  Google Scholar 

  55. Z. Sharifi, F. Tajic, M. Hamzavi, S.M. Ikhdair, Z. Naturf. A 70, 499 (2015)

    Article  Google Scholar 

  56. A.A. Stahlhofen, J. Phys. A: Math. Gen. 37, 10129 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  57. J. Karwowski, H.A. Witek, Theor. Chem. Acc. 133, 1494 (2014)

    Article  Google Scholar 

  58. J. Karwowski, J. Phys.: Conf. Ser. 104, 012033 (2008)

    Google Scholar 

  59. S.-H. Dong, Int. J. Theor. Phys. 40, 559 (2001)

    Article  Google Scholar 

  60. S.-H. Dong, G.-H. San, Found. Phys. Lett. 16, 357 (2003)

    Article  MathSciNet  Google Scholar 

  61. S.-H. Dong, Wave Eequations in Higher Dimensions (Springer, 2011)

  62. G.-H. Sun, S.-H. Dong, K.D. Launey, T. Dytrych, J.P. Draayer, Int. J. Quantum Chem. 115, 891 (2015)

    Article  Google Scholar 

  63. S. Dong, Q. Fang, B.J. Falaye, G.-H. Sun, C. Yáñez-Márquez, S.-H. Dong, Mod. Phys. Lett. A 31, 1650017 (2016)

    Article  ADS  Google Scholar 

  64. S. Dong, G.-H. Sun, B.J. Falaye, S.-H. Dong, Eur. Phys. J. Plus 131, 176 (2016)

    Article  Google Scholar 

  65. M. Hamzavi, S.M. Ikhdair, B.J. Falaye, Ann. Phys. 341, 153 (2014)

    Article  ADS  Google Scholar 

  66. S.M. Ikhdair, M. Hamzavi, Phys. B 407, 4198 (2012)

    Article  ADS  Google Scholar 

  67. E. Grourgoulhon, 3+1 Formalism in General Relativity: Bases of Numerical Relativity (Springer-Verlag, 2012)

  68. I. Ahmadi Azar, Mathematical Methods in Physics, Vol. 1 (Imam Hossein University Press, Iran, 2005) (Persian Language)

  69. M. Bordag, N. Khusnutdinov, Class. Quantum Grav. 13, L41 (1996)

    Article  ADS  Google Scholar 

  70. S. Yu Slavyanov, W. Lay, Special Functions: A Unifield Theory Based in Singularities (Oxford University Press, New York, 2000)

  71. R.K. Patria, Statistical Mechanics, 1st ed. (Pergamon Press, Oxford, 1972)

  72. K.-C. Lee, arXiv:cond-mat/9411040v1 (1994)

  73. M. Ochi, Applied Probability & Stochastic Processes (John Wiley & Sons, 1992)

  74. G. Zitkovic, Lecture 8: Characteristic functions (2013) p. 5, www.ma.utexas.edu/users/gordanz/notes/characteristic.pdf

  75. J. Yi, P. Talkner, Phys. Rev. E 83, 041119 (2011)

    Article  ADS  Google Scholar 

  76. P. Talkner, E. Lutz, P. Hanggi, Phys. Rev. E 75, 050102(R) (2007)

    Article  ADS  Google Scholar 

  77. P. Talkner, P. Hanggi, J. Phys. A 40, F569 (2007)

    Article  ADS  Google Scholar 

  78. M.-A. Dariescu, C. Dariescu, J. Phys.: Condens. Matter 19, 256203 (2007)

    ADS  Google Scholar 

  79. M.-A. Dariescu, C. Dariescu, Chaos, Solitons Fractals 33, 776 (2007)

    Article  ADS  Google Scholar 

  80. N. Byers, C.N. Yang, Phys. Rev. Lett. 7, 46 (1961)

    Article  ADS  Google Scholar 

  81. X.T. Hu, L.H. Zhang, C.S. Jia, J. Mol. Spectrosc. 297, 21 (2014)

    Article  ADS  Google Scholar 

  82. J.Y. Liu, G.D. Zhang, C.S. Jia, Phys. Lett. A 377, 1444 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  83. E.R. Figueiredo Medeiros, E.R. Bezerra de Mello, Eur. Phys. J. C 72, 2051 (2012)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Young Researchers and Elite club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    M. Eshghi

  2. Faculty of Physics, Semnan University, Semnan, Iran

    H. Mehraban

Authors
  1. M. Eshghi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Mehraban
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Eshghi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eshghi, M., Mehraban, H. Study of a 2D charged particle confined by a magnetic and AB flux fields under the radial scalar power potential. Eur. Phys. J. Plus 132, 121 (2017). https://doi.org/10.1140/epjp/i2017-11379-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2017-11379-x

Search

Navigation