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Languages of publication
Abstracts
We consider the dispersion of energy levels for both standard and inverted quantum harmonic oscillators in the presence of a uniform electromagnetic field. For this analysis we use a solution of the corresponding eigenproblem in terms of the Kummer functions. We find a complete description of the energy levels for a particle of mass m and electric charge q subject to the action of a harmonic oscillator and simultaneous uniform magnetic and electric fields. We also analyze the effect of spin on energy levels for an electron.
Discipline
- 03.50.De: Classical electromagnetism, Maxwell equations(for applied classical electromagnetism, see 41.20.-q)
- 02.30.Gp: Special functions
- 03.65.-w: Quantum mechanics[see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics]
Journal
Year
Volume
Issue
Pages
94-96
Physical description
Dates
published
2017-07
Contributors
author
- Department of Mathematics and Physics, Szczecin University, Wielkopolska 15, 70-415 Szczecin, Poland
author
- Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland
References
- [1] L.D. Landau, Z. Phys. 45, 430 (1927), doi: 10.1007/BF01397213
- [2] G. Konstantinou, K. Maulopoulos, 2016 http://arXiv.org/abs/1609.00041v1
- [3] T. Kramer, C. Bracher, M. Kleber, J. Opt. B Quant. Semiclass. Opt. 6, 21 (2004), doi: 10.1088/1464-4266/6/1/004
- [4] T.K. Rebane, Teor. Eksp. Khim. 5, 3 (1969)
- [5] T.K. Rebane, Opt. Spectrosc. 112, 813 (2012), doi: 10.1134/S0030400X12060161
- [6] Q.-G. Lin, Commun. Theor. Phys. 38, 667 (2002)
- [7] I.D. Vagner, V.M. Gvozdikov, P. Wyder, HIT J. Sci. Eng. A 3, 5 (2006)
- [8] Wei Gao-Feng, Long Chao-Yun, Long Zheng-Wen, Qin Shui-Jie, Chin. Phys. C 32, 247 (2008), doi: 10.1088/1674-1137/32/4/001
- [9] T. Taychatanapat, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, Nat. Phys. 7, 621 (2011), doi: 10.1038/nphys2008
- [10] M. Serbyn, D.A. Abanin, Phys. Rev. B 87, 115422 (2013), doi: 10.1103/PhysRevB.87.115422
- [11] L.D. Landau, E.M. Lifshitz, Quantum Mechanics, Non-Relativistic Theory, Pergamon Press, Oxford 1965
- [12] G. Barton, Ann. Phys. 166, 322 (1986), doi: 10.1016/0003-4916(86)90142-9
- [13] W. Miller, Symmetry and Separation of Variables, in series Encyclopedia of Mathematics and Its Applications, Addison-Wesley, Reading (MA) 1977
- [14] I.A. Pedrosa, I. Guedes, Int. J. Mod. Phys. B 18, 1379 (2004), doi: 10.1142/S0217979204024732
- [15] Problems and Solutions on Quantum Mechanics, Ed. Yung-Kuo Lim, World Sci., Singapore 1998
- [16] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series 55, 1972
- [17] H. Buchholz, The Confluent Hypergeometric Function, Springer-Verlag, Berlin 1969
- [18] E.T. Whittaker, G.N. Watson, A Course in Modern Analysis, Cambridge University Press, Cambridge (UK) 1996
- [19] P.A.M. Dirac, Proc. R. Soc. A 117, 610 (1928), doi: 10.1098/rspa.1928.0023
- [19a] P.A.M. Dirac, Proc. R. Soc. A 118, 351 (1928), doi: 10.1098/rspa.1928.0056
- [20] O. Boyarkin, Advanced Particle Physics: Particles, Fields, and Quantum Electrodynamics Vol. 1, Taylor and Francis, 2011
- [21] V.W. Hughes, T. Kinoshita, Rev. Mod. Phys. 71, 133 (1999), doi: 10.1007/978-1-4612-1512-7_14
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv132n1p22kz