On a neutral particle with permanent magnetic dipole moment in a magnetic medium

  • K. BakkeEmail author
  • C. Salvador
Regular Article


We investigate quantum effects that stem from the interaction of a permanent magnetic dipole moment of a neutral particle with an electric field in a magnetic medium. We consider a long non-conductor cylinder that possesses a uniform distribution of electric charges and a non-uniform magnetization. We discuss the possibility of achieving this non-uniform magnetization from the experimental point of view. Besides, due to this non-uniform magnetization, the permanent magnetic dipole moment of the neutral particle also interacts with a non-uniform magnetic field. This interaction gives rise to a linear scalar potential. Then, we show that bound states solutions to the Schrödinger-Pauli equation can be achieved.


  1. 1.
    X.-G. He, B.h.J. McKellar, Phys. Rev. A 47, 3424 (1983)ADSCrossRefGoogle Scholar
  2. 2.
    M. Wilkens, Phys. Rev. Lett. 72, 5 (1994)ADSCrossRefGoogle Scholar
  3. 3.
    Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Peshkin, A. Tonomura, The Aharonov-Bohm Effect, in Lecture Notes in Physics, Vol. 340 (Springer-Verlag, Berlin, 1989)Google Scholar
  5. 5.
    S. Oh, C.-M. Ryu, Phys. Rev. B 51, 13441 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    H. Mathur, A.D. Stone, Phys. Rev. B 44, 10957 (1991)ADSCrossRefGoogle Scholar
  7. 7.
    H. Mathur, A.D. Stone, Phys. Rev. Lett. 68, 2964 (1992)ADSCrossRefGoogle Scholar
  8. 8.
    A.V. Balatsky, B.L. Altshuler, Phys. Rev. Lett. 70, 1678 (1993)ADSCrossRefGoogle Scholar
  9. 9.
    T. Choi, S.Y. Cho, C.-M. Ryu, C.K. Kim, Phys. Rev. B 56, 4825 (1996)ADSCrossRefGoogle Scholar
  10. 10.
    S.-Q. Shena, Z.-J. Li, Z. Ma, Appl. Phys. Lett. 84, 996 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    K. Bakke, C. Furtado, J. Math. Phys. 53, 023514 (2012)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    K. Bakke, C. Furtado, Mod. Phys. Lett. A 26, 1331 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    P.M.T. Barboza, K. Bakke, Ann. Phys. (N.Y.) 361, 259 (2015)CrossRefGoogle Scholar
  14. 14.
    P.M.T. Barboza, K. Bakke, Ann. Phys. (N.Y.) 372, 457 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    L.D. Landau, E.M. Lifshitz, Quantum Mechanics, The Nonrelativistic Theory, 3rd edition (Pergamon, Oxford, 1977)Google Scholar
  16. 16.
    M. Ericsson, E. Sjöqvist, Phys. Rev. A 65, 013607 (2001)ADSCrossRefGoogle Scholar
  17. 17.
    L.R. Ribeiro, C. Furtado, J.R. Nascimento, Phys. Lett. A 348, 135 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    C. Furtado, J.R. Nascimento, L.R. Ribeiro, Phys. Lett. A 358, 336 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    C.F.L. Godinho, J.A. Helayël Neto, Ann. Phys. (Berlin) 528, 597 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    A. Poux, L.R.S. Araújo, C. Filgueiras, F. Moraes, Eur. Phys. J. Plus 129, 100 (2014)CrossRefGoogle Scholar
  21. 21.
    B. Basu, D. Chowdhury, Ann. Phys. (N.Y.) 335, 47 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    L.R. Ribeiro, C. Furtado, E. Passos, J. Phys. G: Nucl. Part. Phys. 39, 105004 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    I.C. Fonseca, K. Bakke, Ann. Phys. (Berlin) 527, 820 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    V.M. Tkachuk, Phys. Rev. A 62, 052112 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    V.M. Tkachuk, Phys. Rev. A 60, 4715 (1999)ADSCrossRefGoogle Scholar
  26. 26.
    D.J. Griffiths, Introduction to Electrodynamics, third edition (Prentice Hall, Upper Saddle River, 1999)Google Scholar
  27. 27.
    J.A.C. Bland, B. Heinrich, Ultrathin Magnetic Structures IV (Springer, Berlin, 1994)Google Scholar
  28. 28.
    A.H. Lu, E.L. Salabas, F. Schüth, Angew. Chem. Int. Ed. 46, 1222 (2007)CrossRefGoogle Scholar
  29. 29.
    P. Schluter, K.H. Wietschorke, W. Greiner, J. Phys. A 16, 1999 (1983)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, UK, 1982)Google Scholar
  31. 31.
    A. Ronveaux, Heun’s Differential Equations (Oxford University Press, Oxford, 1995)Google Scholar
  32. 32.
    D.J. Griffiths, Introduction to Quantum Mechanics, 2nd edition (Prentice Hall, Upper Saddle River, NJ, 2004)Google Scholar
  33. 33.
    G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists, sixth edition (Elsevier Academic Press, New York, 2005)Google Scholar
  34. 34.
    H. Kleinert, Gauge Fields in Condensed Matter, Vol. 2 (World Scientific, Singapore, 1989)Google Scholar
  35. 35.
    M.O. Katanaev, I.V. Volovich, Ann. Phys. (N.Y.) 216, 1 (1992)ADSCrossRefGoogle Scholar
  36. 36.
    K.C. Valanis, V.P. Panoskaltsis, Acta Mech. 175, 77 (2005)CrossRefGoogle Scholar
  37. 37.
    K. Bakke, J.R. Nascimento, C. Furtado, Phys. Rev. D 78, 064012 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Federal da ParaíbaJoão Pessoa, PBBrazil

Personalised recommendations