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

• Authors: Irina Petreska , Trifce Sandev , Zlatko Nedelkoski , Ljupco Pejov
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

three-dimensional anisotropic harmonic oscillator; degeneracy removing; selection rules; stationary perturbation theory

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 4
• Pages: 412-422

Dates

published

1 - 4 - 2013

online

22 - 5 - 2013

Contributors

author

Irina Petreska

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

author

Trifce Sandev

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

author

Zlatko Nedelkoski

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

author

Ljupco Pejov

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

References

• [1] M. Amirfakhrian, M. Hamzavi, Mol. Phys. 110, 2173 (2012) http://dx.doi.org/10.1080/00268976.2012.668227[Crossref]
• [2] A. Durmus, J. Phys. A: Math. Theor. 44, 155205 (2011) http://dx.doi.org/10.1088/1751-8113/44/15/155205[Crossref]
• [3] J. Zhou, H.-Y. Fan, J. Song, Int. J. Theor. Phys. 50, 3149 (2011) http://dx.doi.org/10.1007/s10773-011-0817-8[Crossref]
• [4] M. Aktas, Int. J. Theor. Phys. 48, 2154 (2009) http://dx.doi.org/10.1007/s10773-009-9993-1[Crossref]
• [5] G.-F. Wei, C.-Y. Long, Z.-W. Long, S.-J. Qin, Chinese Phys. C 32, 247 (2008) http://dx.doi.org/10.1088/1674-1137/32/4/001[Crossref]
• [6] S.M. Al-Jaber, Int. J. Theor. Phys. 47, 1853 (2008) http://dx.doi.org/10.1007/s10773-007-9630-9[Crossref]
• [7] W.C. Qiang, S.H. Dong, Phys. Scripta 70, 276 (2004) http://dx.doi.org/10.1088/0031-8949/70/5/002[Crossref]
• [8] M.-L. Liang, W.-Q. Zhang, Int. J. Theor. Phys. 42, 2881 (2003) http://dx.doi.org/10.1023/B:IJTP.0000006015.05376.6b[Crossref]
• [9] J. Main, M. Schwacke, G. Wunner, Phys. Rev. A 57, 1149 (1998) http://dx.doi.org/10.1103/PhysRevA.57.1149[Crossref]
• [10] L. F. Urrutia, C. Manterola, Int. J. Theor. Phys. 25, 75 (1986) http://dx.doi.org/10.1007/BF00669715[Crossref]
• [11] H. Ciftci, R.L. Hall, N. Saad, Cent. Eur. J. Phys. 11, 37 (2013) http://dx.doi.org/10.2478/s11534-012-0147-3[Crossref]
• [12] S.M. Ikhdair, R. Sever, Cent. Eur. J. Phys. 6, 697 (2008) http://dx.doi.org/10.2478/s11534-008-0060-y[Crossref]
• [13] X.-Y. Gu, J.-Q. Sun, J. Math. Phys. 51, 022106 (2010) http://dx.doi.org/10.1063/1.3290739[Crossref]
• [14] M.R. Pahlavani, S.A. Alavi, Commun. Theor. Phys. 58, 739 (2012) http://dx.doi.org/10.1088/0253-6102/58/5/19[Crossref]
• [15] B.J. Falaye, Cent. Eur. J. Phys. 10, 960 (2012) http://dx.doi.org/10.2478/s11534-012-0047-6[Crossref]
• [16] I. Petreska, Gj. Ivanovski, Lj. Pejov, Spectrochim. Acta A 66, 985 (2007) http://dx.doi.org/10.1016/j.saa.2006.05.010[Crossref]
• [17] T. Sandev, I. Petreska, Maced. J. Chem. Chem. En. (formerly Bull. Chem. Technol. Macedonia) 24, 143 (2005)
• [18] I. Petreska, T. Sandev, Gj. Ivanovski, Lj. Pejov, Commun. Theor. Phys. 54, 138 (2010) http://dx.doi.org/10.1088/0253-6102/54/1/26[Crossref]
• [19] A. Sommerfeld, Wave Mechanics (E.P. Dutton and Co. Inc., New York, 1930)
• [20] L. Pauling, E. Bright Wilson Jr, Introduction to Quantum Mechanics with Applications to Chemistry (The McGraw-Hill Book Co., New York, 1935)
• [21] L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Pergamon Press, London, 1958)
• [22] V. Fock, Z. Phys. 47, 446 (1928) http://dx.doi.org/10.1007/BF01390750[Crossref]
• [23] S. M. Ikhadir, M. Hamzavi, R. Sever, Physica B 407, 4523 (2012) http://dx.doi.org/10.1016/j.physb.2012.08.013[Crossref]
• [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) http://dx.doi.org/10.1007/978-3-642-61995-3[Crossref]

Identifiers

DOI

10.2478/s11534-013-0196-2