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Abstracts
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
Journal
Year
Volume
Issue
Pages
1226-1234
Physical description
Dates
published
2014-12
received
2014-03-27
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