Reexamining Larmor precession in a spin-rotator: testable correction and its ramifications

Abstract

For a spin-polarized plane wave passing through a spin-rotator containing uniform magnetic field, we provide a detailed analysis for solving the appropriate Schrödinger equation. A modified expression for spin precession is obtained which reduces to the standard Larmor precession relation when kinetic energy is very large compared to the spin-magnetic field interaction. We show that there are experimentally verifiable regimes of departure from the standard Larmor precession formula. The treatment is then extended to the case of a spin-polarized wave packet passing through a uniform magnetic field. The results based on the standard expression for Larmor precession and that obtained from the modified formula are compared in various regimes of the experimental parameters.

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

References

  1. 1.

    F. Mezei, Z. Phys. 255, 146 (1972)

    ADS  Article  Google Scholar 

  2. 2.

    A. Zeilinger, C.G. Shull, Phys. Rev. B 19, 3957 (1979)

    ADS  Article  Google Scholar 

  3. 3.

    Neutron Spin Echo, edited by F. Mezei (Springer, Berlin, 1980), Vol. 128

  4. 4.

    B. Alefeld, G. Badurek, H. Rauch, Phys. Lett. A 83, 32 (1981)

    ADS  Article  Google Scholar 

  5. 5.

    A.P. Heberle, W.W. Rühle, K. Ploog, Phys. Rev. Lett. 72, 3887 (1994)

    ADS  Article  Google Scholar 

  6. 6.

    Y. Otake, C.M.E. Zeyen, M. Forte, J. Neutron Res. 4, 215 (1996)

    Article  Google Scholar 

  7. 7.

    M. Hino et al., Phys. Rev. A 59, 2261 (1999)

    ADS  Article  Google Scholar 

  8. 8.

    M.T. Rekveldt, T. Keller, R. Golub, Europhys. Lett. 54, 342 (2001)

    ADS  Article  Google Scholar 

  9. 9.

    N. Martina et al., Phys. B: Condens. Matter 406, 2333 (2011) and references therein

    ADS  Article  Google Scholar 

  10. 10.

    A.I. Baz, Sov. J. Nucl. Phys. 4, 182 (1967)

    Google Scholar 

  11. 11.

    A.I. Baz, Sov. J. Nucl. Phys. 5, 161 (1967)

    Google Scholar 

  12. 12.

    V.F. Rybachenko, Sov. J. Nucl. Phys. 54, 635 (1967)

    Google Scholar 

  13. 13.

    M. Buttiker, R. Landauer, Phys. Rev. Lett. 49, 1739 (1982)

    ADS  Article  Google Scholar 

  14. 14.

    M. Buttiker, Phys. Rev. B 27, 6178 (1983)

    ADS  Article  Google Scholar 

  15. 15.

    J.P. Falck, E.H. Hauge, Phys. Rev. B 38, 3287 (1988)

    ADS  Article  Google Scholar 

  16. 16.

    L.D. Landau, E.M. Lifshitz, Quantum Mechanics – Nonrelativistic Theory (Pergamon Press, Oxford, 1965), p. 57

  17. 17.

    J.J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, Reading, 1985), pp. 76–78

  18. 18.

    E. Merzbacher, Quantum Mechanics (John Wiley & Sons, New York, 1961), pp. 26–27

  19. 19.

    C. Cohen-Tanoudji, B. Diu, F. Laloe, Quantum Mechanics (Wiley, London, 1977), p. 403

  20. 20.

    D. Bohm, Quantum Theory (Prentice-Hall, New York, 1951), p. 443

  21. 21.

    W. Greiner, Quantum Mechanics (Springer, Berlin, 2001)

  22. 22.

    D.J. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, Upper Saddle River, 2004)

  23. 23.

    A.K. Pan, M.M. Ali, D. Home, Phys. Lett. A 352, 296 (2006)

    ADS  MATH  Article  Google Scholar 

  24. 24.

    J.G. Muga, C.R. Leavens, Phys. Rep. 338, 353 (2000)

    MathSciNet  ADS  Article  Google Scholar 

  25. 25.

    Time in Quantum Mechanics, edited by J.G. Muga, R. Sala Mayato, I.L. Egusquiza (Springer-Verlag, Berlin, 2002)

  26. 26.

    H. Salecker, E.P. Wigner, Phys. Rev. 109, 571 (1958)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  27. 27.

    A. Peres, Am. J. Phys. 48, 552 (1980)

    MathSciNet  ADS  Article  Google Scholar 

  28. 28.

    P.C.W. Davies, Class. Quantum Grav. 21, 2761 (2004)

    ADS  MATH  Article  Google Scholar 

  29. 29.

    Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, H. Rauch, Nature 425, 45 (2003)

    ADS  Article  Google Scholar 

  30. 30.

    Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, H. Rauch, J. Opt. B: Quantum Semicl. Opt. 6, S7 (2004)

    ADS  Article  Google Scholar 

  31. 31.

    S. Basu, S. Bandyopadhyay, G. Kar, D. Home, Phys. Lett. A 279, 281 (2001)

    MathSciNet  ADS  MATH  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding authors

Correspondence to Alok Kumar Pan or Arka Banerjee.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Home, D., Pan, A. & Banerjee, A. Reexamining Larmor precession in a spin-rotator: testable correction and its ramifications. Eur. Phys. J. D 67, 72 (2013). https://doi.org/10.1140/epjd/e2013-30346-9

Download citation

Keywords

  • Atomic Physics