PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 1 | 78-88
Tytuł artykułu

Path integral treatment of a noncentral electric potential

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a rigorous path integral treatment of a dynamical system in the axially symmetric potential $V(r,\theta ) = V(r) + \tfrac{1} {{r^2 }}V(\theta ) $ . It is shown that the Green’s function can be calculated in spherical coordinate system for $V(\theta ) = \frac{{\hbar ^2 }} {{2\mu }}\frac{{\gamma + \beta \sin ^2 \theta + \alpha \sin ^4 \theta }} {{\sin ^2 \theta \cos ^2 \theta }} $ . As an illustration, we have chosen the example of a spherical harmonic oscillator and also the Coulomb potential for the radial dependence of this noncentral potential. The ring-shaped oscillator and the Hartmann ring-shaped potential are considered as particular cases. When α = β = γ = 0, the discrete energy spectrum, the normalized wave function of the spherical oscillator and the Coulomb potential of a hydrogen-like ion, for a state of orbital quantum number l ≥ 0, are recovered.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
1
Strony
78-88
Opis fizyczny
Daty
wydano
2013-01-01
online
2013-01-15
Twórcy
autor
  • Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université Mentouri, Route d’Ain El Bey, Constantine, Algeria
  • Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université Mentouri, Route d’Ain El Bey, Constantine, Algeria
autor
  • Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université Mentouri, Route d’Ain El Bey, Constantine, Algeria, guechilarbi@yahoo.fr
autor
  • Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université Mentouri, Route d’Ain El Bey, Constantine, Algeria
Bibliografia
  • [1] H. Hartmann, Theor. Chim. Acta 24, 201 (1972) http://dx.doi.org/10.1007/BF00641399[Crossref]
  • [2] H. Hartmann, R. Schuck, J. Radtke, Theor. Chim. Acta 42, 1 (1976) http://dx.doi.org/10.1007/BF00548285[Crossref]
  • [3] H. Hartmann, D. Schuch, Int. J. Quantum Chem. 18, 125 (1980) http://dx.doi.org/10.1002/qua.560180119[Crossref]
  • [4] C. Quesne, J. Phys. A 21, 3093 (1988) http://dx.doi.org/10.1088/0305-4470/21/14/010[Crossref]
  • [5] M.V. Carpio, A. Inomata, In: Path integrals from meV to MeV, eds. M.C. Gutzwiller, A. Inomata, J. Klauder, L. Streit (World Scientific, Singapore, 1986) 261
  • [6] I. Sokmen, Phys. Lett. A 115, 249 (1986) http://dx.doi.org/10.1016/0375-9601(86)90546-3[Crossref]
  • [7] L. Chetouani, L. Guechi, T. F. Hammann, Phys. Lett. A 125, 277 (1987) http://dx.doi.org/10.1016/0375-9601(87)90142-3[Crossref]
  • [8] M. Kibler, T. Negadi, Int. J. Quantum Chem. 26, 405 (1984) http://dx.doi.org/10.1002/qua.560260308[Crossref]
  • [9] C.C. Gerry, Phys. Lett. A 118, 445 (1986) http://dx.doi.org/10.1016/0375-9601(86)90748-6[Crossref]
  • [10] M. Kibler, P. Winternitz, J. Phys. Math. Gen. 20, 4097 (1987) http://dx.doi.org/10.1088/0305-4470/20/13/018[Crossref]
  • [11] A. Guha, S. Mukherjee, J. Math. Phys. 28, 840 (1987) http://dx.doi.org/10.1063/1.527573[Crossref]
  • [12] A.N. Vaidya, H. Boschi Filho, J. Math. Phys. 31, 1951 (1990) http://dx.doi.org/10.1063/1.528643[Crossref]
  • [13] L. Chetouani, L. Guechi, T. F. Hammann, J. Math. Phys. 33, 3410 (1992) http://dx.doi.org/10.1063/1.529889[Crossref]
  • [14] A.A. Makarov, J.A. Smorodinsky, Kh. Valiev, P. Winternitz, Nuovo Cimento A 52, 1061 (1967) http://dx.doi.org/10.1007/BF02755212[Crossref]
  • [15] N.W. Evans, Phys. Lett. A 147, 483 (1990) http://dx.doi.org/10.1016/0375-9601(90)90611-Q[Crossref]
  • [16] N.W. Evans, Phys. Rev. A 41, 5666 (1990) http://dx.doi.org/10.1103/PhysRevA.41.5666[Crossref]
  • [17] N.W. Evans, J. Math. Phys. 31, 600 (1990) http://dx.doi.org/10.1063/1.528895[Crossref]
  • [18] C. Grosche, G.S. Pogosyan, A.N. Sissakian, Fortschr. Phys. 43, 453 (1995) http://dx.doi.org/10.1002/prop.2190430602[Crossref]
  • [19] L. Chetouani, L. Guechi, T. F. Hammann, J. Math. Phys. 42, 4684 (2001) http://dx.doi.org/10.1063/1.1396635[Crossref]
  • [20] C. Berkdemir, J. Math. Chem. 46, 139 (2009) http://dx.doi.org/10.1007/s10910-008-9447-7[Crossref]
  • [21] M.C. Zhang, G.H. Sun, S.H. Dong, Phys. Lett. A 374, 704 (2010) http://dx.doi.org/10.1016/j.physleta.2009.11.072[Crossref]
  • [22] A. Arda, R. Sever, J. Math. Chem. 50, 1484 (2012) http://dx.doi.org/10.1007/s10910-012-9984-y[Crossref]
  • [23] I.H. Duru, Phys. Rev. D 30, 2121 (1984) http://dx.doi.org/10.1103/PhysRevD.30.2121[Crossref]
  • [24] M. Bohm, G. Junker, J. Math. Phys. 28, 1978 (1987) http://dx.doi.org/10.1063/1.527460[Crossref]
  • [25] L. Chetouani, L. Guechi, M. Letlout, T.F. Hammann, Nuovo Cimento B 105, 387 (1990) http://dx.doi.org/10.1007/BF02728821[Crossref]
  • [26] I.S. Gradshtein, I.M. Ryzhik, Tables of Integrals, Series and Products (Academic Press, New York, 1965)
  • [27] B.S. Dewitt, Rev. Mod. Phys. 29, 377 (1957) http://dx.doi.org/10.1103/RevModPhys.29.377[Crossref]
  • [28] D.W. Mc Laughlin, L.S. Schulman, J. Math. Phys. 12, 2520 (1971) http://dx.doi.org/10.1063/1.1665567[Crossref]
  • [29] I.H. Duru, H. Kleinert, Phys. Lett. B 84, 185 (1979) http://dx.doi.org/10.1016/0370-2693(79)90280-6[Crossref]
  • [30] I.H. Duru, H. Kleinert, Fortschr. Phys., 30, 401 (1982) http://dx.doi.org/10.1002/prop.19820300802[Crossref]
  • [31] D. Peak, A. Inomata, J. Math. Phys. 10, 1422 (1969) http://dx.doi.org/10.1063/1.1664984[Crossref]
  • [32] M.V. Carpio-Bernido, C.C. Bernido, Phys. Lett. A 134, 395 (1989) http://dx.doi.org/10.1016/0375-9601(89)90357-5[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-012-0125-9
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.