PL EN


Preferences help
enabled [disable] Abstract
Number of results
2014 | 126 | 6 | 1226-1234
Article title

Relativistic Generalizations of the Quantum Harmonic Oscillator

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
We investigate the dynamics of the spin-less relativistic particle subject to an external field of a harmonic oscillator potential. The Klein-Gordon equation with one- and three-dimensional vector and scalar parabolic potentials is solved using the expansion of the wavefunction in properly selected basis-sets. The resonance states are determined using the complex coordinate rotation method. The analytic expressions for the first- and second-order relativistic energy corrections are derived perturbatively. The relativistic model of the harmonic oscillator in the momentum representation, originally proposed by Znojil, is also discussed.
Keywords
EN
Contributors
author
  • Department of Physics and Computer Methods, University of Warmia and Mazury in Olsztyn, Słoneczna 54, 10-710 Olsztyn, Poland
References
  • [1] A. Beléndez, D.I. Méndez, M.L. Alvarez, C. Pascual, T. Beléndez, Int. J. Mod. Phys. B 23, 521 (2009), doi: 10.1142/S0217979209049954
  • [2] K. Nikolsky, Z. Phys. 62, 677 (1930), doi: 10.1007/BF01843485
  • [3] I. Postępska, Acta Phys. Pol. 4, 269 (1935)
  • [4] P.A. Cook, Lett. Nuovo Cimento 10, 419 (1971), doi: 10.1007/BF02785170
  • [5] A.L. Harvey, Phys. Rev. D 6, 1474 (1972), doi: 10.1103/PhysRevD.6.1474
  • [6] M. Sachs, Lett. Nuovo Cimento 13, 169 (1975), doi: 10.1007/BF02742604
  • [7] M. Moshinsky, A. Szczepaniak, J. Phys. A Math. Gen. 22, L817 (1989), doi: 10.1088/0305-4470/22/17/002
  • [8] M. Znojil, J. Phys. A Math. Gen. 29, 2905 (1996), doi: 10.1088/0305-4470/29/11/024
  • [9] F.M. Toyama, Y. Nogami, Phys. Rev. A 59, 1056 (1999), doi: 10.1103/PhysRevA.59.1056
  • [10] LMC R. Lisboa, M. Malherio, A.S. de Castro, P. Alberto, M. Fiolhais, Phys. Rev. C 69, 024319 (2004), doi: 10.1103/PhysRevC.69.024319
  • [11] J. Karwowski, G. Pestka, Theoret. Chem. Account 118, 519 (2007), doi: 10.1007/s00214-007-0362-y
  • [12] A. Rao Nagalakshim, B.A. Kagali, Phys. Scr. 77, 015003 (2008), doi: 10.1088/0031-8949/77/01/015003
  • [13] I. Bars, Phys. Rev. D 79, 045009 (2009), doi: 10.1103/PhysRevD.79.045009
  • [14] A. Poszwa, Phys. Rev. A 82, 052110 (2010), doi: 10.1103/PhysRevA.82.052110
  • [15] A. Boumali, A. Haldallah, A. Toumi, Phys. Scr. 84, 037001 (2011), doi: 10.1088/0031-8949/84/03/037001
  • [16] A.S. Larkin, V.S. Filinov, Phys. Lett. A 377, 1171 (2013), doi: 10.1016/j.physleta.2013.03.019
  • [17] J. Benítez, R.P. Martnez y Romero, H. N. Núez-Yépez, A.L. Salas-Brito Phys. Rev. Lett. 64, 1643 (1990), doi: 10.1103/PhysRevLett.64.1643
  • [18] P. Rozmej, R. Arveu, J. Phys. A Math. Gen. 32, 5367 (1999), doi: 10.1088/0305-4470/32/28/314
  • [19] M.H. Pacheco, R.R. Landim, C.A.S. Almeida, Phys. Lett. A 311, 93 (2003), doi: 10.1016/S0375-9601(03)00467-5
  • [20] W. Chunfeng, X. Kang, Int. J. Theor. Phys. 43, 2395 (2004), doi: 10.1007/s10773-004-7706-3
  • [21] R. Rekioua, T. Boudjedaa, Eur. Phys. J. C 49, 1091 (2007), doi: 10.1140/epjc/s10052-006-0169-3
  • [22] A. Bermudez, M.A. Martin-Delgado, E. Solano, Phys. Rev. A 76, 041801(R) (2007), doi: 10.1103/PhysRevA.76.041801
  • [23] R. De Lima Rodrigues, Phys. Lett. A 372, 2587 (2008), doi: 10.1016/j.physleta.2007.12.070
  • [24] N.A. Rao, B.A. Kagali, Phys. Scr. 77, 015003 (2008), doi: 10.1088/0031-8949/77/01/015003
  • [25] A. Boumali, A. Halfdallah, A. Toumi, Phys. Scr. 84, 037001 (2011), doi: 10.1088/0031-8949/84/03/037001
  • [26] A.D. Alhaidari, H. Bahlouli, A. Al-Hasan, Phys. Lett. A 349, 87 (2006), doi: 10.1016/j.physleta.2005.09.008
  • [27] M.K. Bahar, F. Yasuk, Adv. High Energy Phys. 2013, 814985 (2013), doi: 10.1155/2013/814985
  • [28] W. Greiner Relativistic Quantum Mechanics, Springer-Verlag, Berlin (2000)
  • [29] G.E. Brown, D.G. Ravenhall, Proc. R. Soc. London, Ser. A 208, 552 (1952)
  • [30] N. Moiseyev Non-Hermitian Quantum Mechanics, Cambridge University Press, New York 2011
  • [31] R.A. Weder, J. Math. Phys. 15, 20 (1974), doi: 10.1063/1.1666495
  • [32] P. Seba, Lett. Math. Phys. 16, 51 (1988), doi: 10.1007/BF00398170
  • [33] G. Pestka, M. Bylicki, J. Karwowski, J. Phys. B At. Mol. Opt. Phys. 39, 2979 (2006), doi: 10.1088/0953-4075/39/14/006
  • [34] M. Abramowitz, I.A. Stegun Handbook of Mathematical Functions Dover, New York 1968
  • [35] I.D. Feranchuk, L.I. Komarov, I.V. Nichipor, A.P. Ulyanenkov, Ann. Phys.-New York 238, 370 (1995), doi: 10.1006/aphy.1995.1025
  • [36] J.N. Ginnocchio, Phys. Rev. Lett. 78, 436 (1997), doi: 10.1103/PhysRevLett.78.436
  • [37] M.M. Panja, R. Dutt, Y.P. Varshini, J. Phys. A Math. Gen. 22, 2991 (1989), doi: 10.1088/0305-4470/22/15/015
  • [38] H. Akcay, R. Sever, Phys. Scr. 89, 015003 (2014), doi: 10.1088/0031-8949/89/01/015003
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv126n602kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.