Skip to main content
SpringerLink
Log in

Axially symmetrical molecules in electric and magnetic fields: energy spectrum and selection rules

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

In this paper we investigate the effects of external electric and magnetic fields on a three-dimensional harmonic oscillator with axial symmetry. The energy spectrum of such a system is non-degenerate due to the presence of the magnetic field. The degeneracy of the energy spectrum in the absence of a magnetic field is discussed. The influence of electric and magnetic fields, as well as the frequencies of the oscillator on the probability distribution function is analyzed. Optical transition probabilities are examined by deriving the selection rules in dipole approximation for the quantum numbers n p , m l and n z . Employing stationary perturbation theory, the effects of deformations of the potential energy function on the oscillatory states are analyzed. Such models have been used in literature in analysis of spectra of axially symmetrical molecules and cylindrical quantum dots.

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. M. Amirfakhrian, M. Hamzavi, Mol. Phys. 110, 2173 (2012)

    Article  ADS  Google Scholar 

  2. A. Durmus, J. Phys. A: Math. Theor. 44, 155205 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  3. J. Zhou, H.-Y. Fan, J. Song, Int. J. Theor. Phys. 50, 3149 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Aktas, Int. J. Theor. Phys. 48, 2154 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. G.-F. Wei, C.-Y. Long, Z.-W. Long, S.-J. Qin, Chinese Phys. C 32, 247 (2008)

    Article  ADS  Google Scholar 

  6. S.M. Al-Jaber, Int. J. Theor. Phys. 47, 1853 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. W.C. Qiang, S.H. Dong, Phys. Scripta 70, 276 (2004)

    Article  ADS  MATH  Google Scholar 

  8. M.-L. Liang, W.-Q. Zhang, Int. J. Theor. Phys. 42, 2881 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Main, M. Schwacke, G. Wunner, Phys. Rev. A 57, 1149 (1998)

    Article  ADS  Google Scholar 

  10. L. F. Urrutia, C. Manterola, Int. J. Theor. Phys. 25, 75 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Ciftci, R.L. Hall, N. Saad, Cent. Eur. J. Phys. 11, 37 (2013)

    Article  Google Scholar 

  12. S.M. Ikhdair, R. Sever, Cent. Eur. J. Phys. 6, 697 (2008)

    Article  Google Scholar 

  13. X.-Y. Gu, J.-Q. Sun, J. Math. Phys. 51, 022106 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  14. M.R. Pahlavani, S.A. Alavi, Commun. Theor. Phys. 58, 739 (2012)

    Article  Google Scholar 

  15. B.J. Falaye, Cent. Eur. J. Phys. 10, 960 (2012)

    Article  Google Scholar 

  16. I. Petreska, Gj. Ivanovski, Lj. Pejov, Spectrochim. Acta A 66, 985 (2007)

    Article  ADS  Google Scholar 

  17. T. Sandev, I. Petreska, Maced. J. Chem. Chem. En. (formerly Bull. Chem. Technol. Macedonia) 24, 143 (2005)

    Google Scholar 

  18. I. Petreska, T. Sandev, Gj. Ivanovski, Lj. Pejov, Commun. Theor. Phys. 54, 138 (2010)

    Article  ADS  MATH  Google Scholar 

  19. A. Sommerfeld, Wave Mechanics (E.P. Dutton and Co. Inc., New York, 1930)

    Google Scholar 

  20. L. Pauling, E. Bright Wilson Jr, Introduction to Quantum Mechanics with Applications to Chemistry (The McGraw-Hill Book Co., New York, 1935)

    Google Scholar 

  21. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Pergamon Press, London, 1958)

    MATH  Google Scholar 

  22. V. Fock, Z. Phys. 47, 446 (1928)

    Article  ADS  MATH  Google Scholar 

  23. S. M. Ikhadir, M. Hamzavi, R. Sever, Physica B 407, 4523 (2012)

    Article  ADS  Google Scholar 

  24. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, eds. Applied Mathematics, Series 55 (National Bureau of Standards, Washington, 1964)

  25. S. Flügge, Practical Quantum Mechanics (Springer-Verlag, Berlin, 1971)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physics, Faculty of Natural Sciences and Mathematics, Saints Cyril and Methodius University, 1000, Skopje, Macedonia

    Irina Petreska & Zlatko Nedelkoski

  2. Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020, Skopje, Macedonia

    Trifce Sandev

  3. Institute of Chemistry, Faculty of Natural Sciences and Mathematics, Saints Cyril and Methodius University, 1000, Skopje, Macedonia

    Ljupco Pejov

Authors
  1. Irina Petreska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Trifce Sandev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zlatko Nedelkoski
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ljupco Pejov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irina Petreska.

About this article

Cite this article

Petreska, I., Sandev, T., Nedelkoski, Z. et al. Axially symmetrical molecules in electric and magnetic fields: energy spectrum and selection rules. centr.eur.j.phys. 11, 412–422 (2013). https://doi.org/10.2478/s11534-013-0196-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11534-013-0196-2

Keywords

Search

Navigation