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

Regular Article

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.

References

  1. 1.
    S. Flugge, Practical Quantum Mechanics (Springer-Verlag, Berlin, Heidelberg, New York, 1974)Google Scholar
  2. 2.
    S.H. Dong, M. Lozada-Cassou, Phys. Lett. A 330, 168 (2004)ADSCrossRefGoogle Scholar
  3. 3.
    M.C. Zhang, G.H. Sun, S.H. Dong, Phys. Lett. A 374, 704 (2010)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    C.S. Jia, Y. Li, Y. Sun, L.T. Sun, Phys. Lett. A 311, 115 (2003)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    L.Z. Yi, Y.F. Diao, J.Y. Liu, C.S. Jia, Phys. Lett. A 333, 212 (2004)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    O. Aydogdu, R. Sever, Ann. Phys. (NY) 325, 373 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    G. Chen, Phys. Lett. A 326, 55 (2004)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Arda, R. Sever, Commun. Theor. Phys. 58, 27 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    S. Ortakaya, Chin. Phys. B 21, 070303 (2012)CrossRefGoogle Scholar
  10. 10.
    A. Ishkhanyan, EPL 115, 20002 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    M. Eshghi, H. Mehraban, S.M. Ikhdair, Acta Math. Appl. Sin. 31, 1131 (2015)CrossRefGoogle Scholar
  12. 12.
    M. Eshghi, H. Mehraban, J. Kor. Phys. Soc. 67, 1118 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    M. Eshghi, H. Mehraban, Chin. J. Phys. 50, 533 (2012)Google Scholar
  14. 14.
    M. Eshghi, H. Mehraban, J. Math. Phys. 57, 082105 (2016)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    M. Eshghi, H. Mehraban, C. R. Phys. 18, 47 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    S.V. Kryuchkov, E.I. Kukhar, Phys. B 445, 93 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    C. Weishbuch, B. Vinter, Quantum Semiconductor Heterostructure (Academic Press, New-York, 1993)Google Scholar
  19. 19.
    C. Frankenberg, J.F. Meiring, M. Van Weele, U. Platt, T. Wagner, Science 308, 1010 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    A. Baura, M. Kumar Sen, B. Chandra Bag, Chem. Phys. 417, 30 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    H. Haken, H.C. Wolf, Molecular Physics and Elements of Quantum Chemistry: Introduction to Experiments and Theory (Springer, Berlin, 1995)Google Scholar
  22. 22.
    A. Arda, R. Sever, J. Math. Chem. 50, 971 (2012)MathSciNetCrossRefGoogle Scholar
  23. 23.
    E.R. Figueiredo Medeiros, E.R. Bezerra de Mello, Eur. Phys. J. C 72, 2051 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    Al.L. Efros, A.L. Efros, Sov. Phys. Semicond. 16, 772 (1982)Google Scholar
  25. 25.
    X. Yao, A. Belyanin, J. Phys.: Condens. Matter. 25, 054203 (2013)ADSGoogle Scholar
  26. 26.
    R. Khordad, Phys. B 406, 620 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    Vl.A. Margulis, E.E. Muryumin, E.A. Gaiduk, J. Opt. 16, 125203 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    W. Xie, S. Liang, Phys. B 406, 4657 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    R. Sever, C. Tezcan, M. Aktas, O. Yesiltas, J. Math. Chem. 43, 845 (2008)MathSciNetCrossRefGoogle Scholar
  30. 30.
    V.A. Harutyunyan, E.M. Kazaryan, H.A. Kostanyan, H.A. Sarkisyan, Phys. E 36, 114 (2007)CrossRefGoogle Scholar
  31. 31.
    B.J. Falaye, G.-H. Sun, R. Silva-Ortigoza, S.H. Dong, Phys. Rev. E 93, 053201 (2016)ADSCrossRefGoogle Scholar
  32. 32.
    N. Raigoza, A.L. Morales, C.A. Duque, Phys. B 363, 262 (2005)ADSCrossRefGoogle Scholar
  33. 33.
    Y. Naim, J. Vahedi, R. Soltani, Opt. Quantum Electron. 47, 2947 (2015)CrossRefGoogle Scholar
  34. 34.
    M.S. Atoyan, E.M. Kazaryan, H.A. Sarkisyan, Physica E 22, 860 (2004)ADSCrossRefGoogle Scholar
  35. 35.
    L.A. Falkovsky, J. Phys.: Conf. Ser. 129, 012004 (2008)Google Scholar
  36. 36.
    A. Ghoshal, Y.K. Ho, Phys. Rev. E 81, 016403 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    M.L. Glasser, N.H. March, L.M. Nieto, Phys. Lett. A 376, 1477 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    S.M. Ikhdair, B.J. Falaye, Chem. Phys. 421, 84 (2013)ADSCrossRefGoogle Scholar
  39. 39.
    V. Santos, R.V. Maluf, C.A.S. Almeida, arXiv:1401.8051v2 (2014)
  40. 40.
    S. Hassanabadi, M. Ghominejad, Adv. High Energy Phys. 2014, 185169 (2014)Google Scholar
  41. 41.
    A. Boumali, H. Hassanabadi, Eur. Phys. J. Plus 128, 124 (2013)CrossRefGoogle Scholar
  42. 42.
    M.S. Reis, S. Soriano, Appl. Phys. Lett. 102, 112903 (2013)ADSCrossRefGoogle Scholar
  43. 43.
    A. Boumali, Phys. Scr. 90, 045702 (2015)ADSCrossRefGoogle Scholar
  44. 44.
    S.-H. Dong, M. Lozada-Cassou, J. Yu, F. Jiménez-Ángeles, A.L. Rivera, Int. J. Quantum Chem. 102, 366 (2007)ADSCrossRefGoogle Scholar
  45. 45.
    S.-H. Dong, M. Cruz-Irisson, J. Math. Chem. 50, 881 (2012)MathSciNetCrossRefGoogle Scholar
  46. 46.
    C.-S. Jia, L.-H. Zhang, C.-W. Wang, Chem. Phys. Lett. 667, 211 (2017)ADSCrossRefGoogle Scholar
  47. 47.
    I.C. Fonseca, K. Bakke, Proc. R. Soc. A 471, 20150362 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    A.B. Oliveira, K. Bakke, Proc. R. Soc. A 472, 20150858 (2016)ADSCrossRefGoogle Scholar
  49. 49.
    K. Bakke, Ann. Phys. 241, 86 (2014)ADSCrossRefGoogle Scholar
  50. 50.
    L.L. Vitoria, K. Bakke, Eur. Phys. J. Plus 131, 36 (2016)CrossRefGoogle Scholar
  51. 51.
    L.L. Vitoria, C. Furtado, K. Bakke, Ann. Phys. 370, 128 (2016)ADSCrossRefGoogle Scholar
  52. 52.
    A. Ronveaux, Heun's Differential Equations (Oxford University Press, Oxford, 1995)Google Scholar
  53. 53.
    M. Eshghi, H. Mehraban, S.M. Ikhdair, Eur. Phys. J. A 52, 201 (2016)ADSCrossRefGoogle Scholar
  54. 54.
    S.M. Ikhdair, B.J. Falaye, M. Hamzavi, Ann. Phys. 353, 282 (2015)ADSCrossRefGoogle Scholar
  55. 55.
    Z. Sharifi, F. Tajic, M. Hamzavi, S.M. Ikhdair, Z. Naturf. A 70, 499 (2015)CrossRefGoogle Scholar
  56. 56.
    A.A. Stahlhofen, J. Phys. A: Math. Gen. 37, 10129 (2004)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    J. Karwowski, H.A. Witek, Theor. Chem. Acc. 133, 1494 (2014)CrossRefGoogle Scholar
  58. 58.
    J. Karwowski, J. Phys.: Conf. Ser. 104, 012033 (2008)Google Scholar
  59. 59.
    S.-H. Dong, Int. J. Theor. Phys. 40, 559 (2001)CrossRefGoogle Scholar
  60. 60.
    S.-H. Dong, G.-H. San, Found. Phys. Lett. 16, 357 (2003)MathSciNetCrossRefGoogle Scholar
  61. 61.
    S.-H. Dong, Wave Eequations in Higher Dimensions (Springer, 2011)Google Scholar
  62. 62.
    G.-H. Sun, S.-H. Dong, K.D. Launey, T. Dytrych, J.P. Draayer, Int. J. Quantum Chem. 115, 891 (2015)CrossRefGoogle Scholar
  63. 63.
    S. Dong, Q. Fang, B.J. Falaye, G.-H. Sun, C. Yáñez-Márquez, S.-H. Dong, Mod. Phys. Lett. A 31, 1650017 (2016)ADSCrossRefGoogle Scholar
  64. 64.
    S. Dong, G.-H. Sun, B.J. Falaye, S.-H. Dong, Eur. Phys. J. Plus 131, 176 (2016)CrossRefGoogle Scholar
  65. 65.
    M. Hamzavi, S.M. Ikhdair, B.J. Falaye, Ann. Phys. 341, 153 (2014)ADSCrossRefGoogle Scholar
  66. 66.
    S.M. Ikhdair, M. Hamzavi, Phys. B 407, 4198 (2012)ADSCrossRefGoogle Scholar
  67. 67.
    E. Grourgoulhon, 3+1 Formalism in General Relativity: Bases of Numerical Relativity (Springer-Verlag, 2012)Google Scholar
  68. 68.
    I. Ahmadi Azar, Mathematical Methods in Physics, Vol. 1 (Imam Hossein University Press, Iran, 2005) (Persian Language)Google Scholar
  69. 69.
    M. Bordag, N. Khusnutdinov, Class. Quantum Grav. 13, L41 (1996)ADSCrossRefGoogle Scholar
  70. 70.
    S. Yu Slavyanov, W. Lay, Special Functions: A Unifield Theory Based in Singularities (Oxford University Press, New York, 2000)Google Scholar
  71. 71.
    R.K. Patria, Statistical Mechanics, 1st ed. (Pergamon Press, Oxford, 1972)Google Scholar
  72. 72.
    K.-C. Lee, arXiv:cond-mat/9411040v1 (1994)
  73. 73.
    M. Ochi, Applied Probability & Stochastic Processes (John Wiley & Sons, 1992)Google Scholar
  74. 74.
    G. Zitkovic, Lecture 8: Characteristic functions (2013) p. 5, www.ma.utexas.edu/users/gordanz/notes/characteristic.pdf
  75. 75.
    J. Yi, P. Talkner, Phys. Rev. E 83, 041119 (2011)ADSCrossRefGoogle Scholar
  76. 76.
    P. Talkner, E. Lutz, P. Hanggi, Phys. Rev. E 75, 050102(R) (2007)ADSCrossRefGoogle Scholar
  77. 77.
    P. Talkner, P. Hanggi, J. Phys. A 40, F569 (2007)ADSCrossRefGoogle Scholar
  78. 78.
    M.-A. Dariescu, C. Dariescu, J. Phys.: Condens. Matter 19, 256203 (2007)ADSGoogle Scholar
  79. 79.
    M.-A. Dariescu, C. Dariescu, Chaos, Solitons Fractals 33, 776 (2007)ADSCrossRefGoogle Scholar
  80. 80.
    N. Byers, C.N. Yang, Phys. Rev. Lett. 7, 46 (1961)ADSCrossRefGoogle Scholar
  81. 81.
    X.T. Hu, L.H. Zhang, C.S. Jia, J. Mol. Spectrosc. 297, 21 (2014)ADSCrossRefGoogle Scholar
  82. 82.
    J.Y. Liu, G.D. Zhang, C.S. Jia, Phys. Lett. A 377, 1444 (2013)ADSMathSciNetCrossRefGoogle Scholar
  83. 83.
    E.R. Figueiredo Medeiros, E.R. Bezerra de Mello, Eur. Phys. J. C 72, 2051 (2012)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Young Researchers and Elite club, Central Tehran BranchIslamic Azad UniversityTehranIran
  2. 2.Faculty of PhysicsSemnan UniversitySemnanIran

Personalised recommendations