Skip to main content
SpringerLink
Log in

Parity-violating effects in an exotic perturbation of the rigid rotator

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

Abstract

The perturbation of the free rigid rotator by the trigonometric Scarf potential is shown to conserve its energy excitation patterns and change only the wave functions towards spherical harmonics rescaled by a function of an unspecified parity, or mixtures of such rescaled harmonics of equal magnetic quantum numbers and different angular momenta. In effect, no parity can be assigned to the states of the rotational bands emerging in this exotic way, and the electric dipole operator is allowed to acquire non-vanishing expectation values.

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. C.D. Harris, M.D. Bertolucci, Symmetry and Spectroscopy (Oxford University Press, 1978).

  2. G.B. Arfken, H.-J. Weber, Mathematical methods for Physicists, 5th edition (Academic Press, 2001).

  3. Mark Kac, Am. Math. Mont. 73, 1 (1966).

    Article  MATH  Google Scholar 

  4. M. Vito Cruz, The spectrum of the Laplacian in Riemannian geometry, preprint 2003, https://math.berkeley.edu/~alanw/240papers03/vitocruz.pdf.

  5. C.S. Gordon, E. Wilson, J. Differ. Geom. 19, 241 (1984).

    MATH  MathSciNet  Google Scholar 

  6. Carolyn S. Gordon, Dorothee Schueth, J. Geom. Analysis 13, 279 (2003) http://www.math.hu-berlin.de/~.

    Google Scholar 

  7. A. Khare, AIP Conf. Proc. 744, 133 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  8. A. Karamtskou, H. Kleinert, Int. J. Geom. Meth. Mod. Phys. 11, 14066 (2014).

    Google Scholar 

  9. S. Gnutzman, U. Smilansky, N. Sondergaard, J. Phys. A: Math. Gen. 38, 8921 (2005).

    Article  ADS  Google Scholar 

  10. F.L. Scarf, Phys. Rev. 109, 2170 (1959).

    Article  ADS  Google Scholar 

  11. G. Pöschl, E. Teller, Z. Phys. 83, 143 (1933).

    Article  ADS  Google Scholar 

  12. R. De, R. Dutt, U. Sukhatme, J. Phys. A: Math. Gen. 25, L843 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  13. E.T. Whittaker, G.N. Watson, A Course of Modern Analysis, 3rd edition (Cambridge University Press, 1920) chapt. X, pp. 194--196.

  14. A.F. Stevenson, Phys. Rev. 59, 842 (1941).

    Article  ADS  Google Scholar 

  15. C. Khari, A. Suprami, J. Appl. Phys. 2, 13 (2012).

    Google Scholar 

  16. Phillipe Dennery, André Krzywicki, Mathematics for Physicists (Dover Publications, Mineola, New York, 1996).

  17. Y. Alhassid, F. Gürsey, F. Yachello, Phys. Rev. Lett. 50, 873 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  18. G. Lévai, F. Cannata, A. Ventura, J. Phys. A: Math. Gen. 35, 5041 (2002).

    Article  ADS  MATH  Google Scholar 

  19. A. Pallares-Rivera, F. de J. Rosales-Aldape, M. Kirchbach, J. Phys. A: Math. Theor. 47, 085303 (2014).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physics, Autonomous University at San Luis Potosi, Av. Manuel Nava 6, University Campus, SLP 78290, San Luis Potosi, Mexico

    A. Pallares-Rivera & M. Kirchbach

Authors
  1. A. Pallares-Rivera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Kirchbach
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Pallares-Rivera.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pallares-Rivera, A., Kirchbach, M. Parity-violating effects in an exotic perturbation of the rigid rotator. Eur. Phys. J. Plus 130, 40 (2015). https://doi.org/10.1140/epjp/i2015-15040-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2015-15040-6

Keywords

Search

Navigation