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Number of results
Journal
2008 | 6 | 3 | 685-696
Article title

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

Content
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Languages of publication
EN
Abstracts
EN
A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $$
V(r,\theta ) = \tfrac{1}
{8}\kappa r_e^2 \left( {\tfrac{r}
{{r_e }} - \tfrac{{r_e }}
{r}} \right)^2 + \tfrac{{\beta cos^2 \theta }}
{{r^2 sin^2 \theta }}
$$. The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.
Publisher
Journal
Year
Volume
6
Issue
3
Pages
685-696
Physical description
Dates
published
1 - 9 - 2008
online
17 - 7 - 2008
References
  • [1] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 21, 6465 (2006) http://dx.doi.org/10.1142/S0217751X06034240[Crossref]
  • [2] S.M. Ikhdair, R. Sever, J. Mol. Struct.-Theochem 809, 103 (2007) http://dx.doi.org/10.1016/j.theochem.2007.01.019[Crossref]
  • [3] S.M. Ikhdair, R. Sever, J. Math. Chem. 41, 329 (2007) http://dx.doi.org/10.1007/s10910-006-9080-2[Crossref]
  • [4] S.M. Ikhdair, R. Sever, J. Math. Chem. 41, 343 (2007) http://dx.doi.org/10.1007/s10910-007-9226-x[Crossref]
  • [5] S. Özçelik, M. Şimşek, Phys. Lett. A 152. 145 (1991) http://dx.doi.org/10.1016/0375-9601(91)91081-N[Crossref]
  • [6] S.-H. Dong, Phys. Scr. 64, 273 (2001) http://dx.doi.org/10.1238/Physica.Regular.064a00273[Crossref]
  • [7] S.-H. Dong, Z.-Q. Ma, J. Phys. A 31, 9855 (1998) http://dx.doi.org/10.1088/0305-4470/31/49/009[Crossref]
  • [8] M.S. Child, S.-H. Dong, X.-G. Wang, J. Phys. A 33, 5653 (2000) http://dx.doi.org/10.1088/0305-4470/33/32/303[Crossref]
  • [9] S.-H. Dong, Int. J. Theor. Phys. 39, 1119 (2000) http://dx.doi.org/10.1023/A:1003614810934[Crossref]
  • [10] S.-H. Dong, Int. J. Theor. Phys. 40, 569 (2001) http://dx.doi.org/10.1023/A:1004171912938[Crossref]
  • [11] S.-H. Dong, Phys. Scr. 65, 289 (2002) http://dx.doi.org/10.1238/Physica.Regular.065a00289[Crossref]
  • [12] S. Flügge, Practical Quantum Mechanics 1 (Springer, Berlin, 1994)
  • [13] L.I. Schiff, Quantum Mechanics 3rd edn (McGraw-Hill Book Co., New York, 1968)
  • [14] L.D. Landau, E.M. Lifshitz, Quantum Mechanics, Nonrelativistic Theory, 3rd edn (Pergamon, New York, 1977)
  • [15] M.M. Neito, Am. J. Phys. 47, 1067 (1979) http://dx.doi.org/10.1119/1.11976[Crossref]
  • [16] I.I. Goldman, V.D. Krivchenkov, Problems in quantum mechanics (Pergamon Press, New York, 1961)
  • [17] Y. Weissman, J. Jortner, Phys. Lett. A 70, 177 (1979) http://dx.doi.org/10.1016/0375-9601(79)90197-X[Crossref]
  • [18] S.M. Ikhdair, R. Sever, arXiv:0801.4857, Int. J. Mod. Phys. C (in print)
  • [19] Ş. Erkoç, R. Sever, Phys. Rev. A 37, 2687 (1988) http://dx.doi.org/10.1103/PhysRevA.37.2687[Crossref]
  • [20] M.L. Sage, Chem. Phys. 87, 431 (1984) http://dx.doi.org/10.1016/0301-0104(84)85123-X[Crossref]
  • [21] M. Sage, J. Goodisman, Am. J. Phys. 53, 350 (1985) http://dx.doi.org/10.1119/1.14408[Crossref]
  • [22] Ş. Erkoç, R. Sever, Phys. Rev. D 30, 2117 (1984) http://dx.doi.org/10.1103/PhysRevD.30.2117[Crossref]
  • [23] Ş. Erkoç, R. Sever, Phys. Rev. D 33, 588 (1986) http://dx.doi.org/10.1103/PhysRevD.33.588[Crossref]
  • [24] I.I. Goldman, V.D. Krivchenkov, V.I. Kogan, V.M. Galitskii, Problems in Quantum Mechanics (Pergamon Press, London, 1960) 8
  • [25] C.J. Ballhausen, Chem. Phys. Lett. 146, 449 (1988) http://dx.doi.org/10.1016/0009-2614(88)87476-1[Crossref]
  • [26] C.J. Ballhausen, Chem. Phys. Lett. 151, 428 (1988) http://dx.doi.org/10.1016/0009-2614(88)85162-5[Crossref]
  • [27] F. Büyükkiliç, D. Demirhan, S.F. Özeren, Chem Phys. Lett. 194, 9 (1992) http://dx.doi.org/10.1016/0009-2614(92)85734-R[Crossref]
  • [28] D. Popov, J. Phys. A: Math. Gen. 34, 5283 (2001)
  • [29] S.-H. Dong, Z.-Q. Ma, Int. J. Mod. Phys. E 11, 155 (2002) http://dx.doi.org/10.1142/S0218301302000752[Crossref]
  • [30] L.-Y. Wang, X.-Y. Gu, Z.-Q. Ma, S.-H. Dong, Found. Phys. Lett. 15, 569 (2002) http://dx.doi.org/10.1023/A:1023937704158[Crossref]
  • [31] S.-H. Dong, App. Math. Lett. 16, 199 (2003) http://dx.doi.org/10.1016/S0893-9659(03)80032-0[Crossref]
  • [32] S. Ikhdair, R. Sever, J. Mol. Struct.-Theochem 806, 155 (2007) http://dx.doi.org/10.1016/j.theochem.2006.11.019[Crossref]
  • [33] S.M. Ikhdair, R. Sever, preprint quant-ph/0611065, to appear in J. Molec. Struct.-Theochem (2008)
  • [34] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. C 18, 1571 (2007) http://dx.doi.org/10.1142/S0129183107011583[Crossref]
  • [35] S.M. Ikhdair, R. Sever, Centr. Eur. J. Phys. 5, 516 (2007) http://dx.doi.org/10.2478/s11534-007-0022-9[Crossref]
  • [36] S.M. Ikhdair, R. Sever, preprint quant-ph/0702052 to appear in the Centr. Eur. J. Phys.
  • [37] H. Hartmann et al., Theor. Chim. Acta 24, 201 (1972) http://dx.doi.org/10.1007/BF00641399[Crossref]
  • [38] H. Hartmann, R. Schuck, J. Radtke, Theor. Chim. Acta 42, 1 (1976) http://dx.doi.org/10.1007/BF00548285[Crossref]
  • [39] H. Hartmann, D. Schuck, Int. J. Quantum Chem. 18, 125 (1980) http://dx.doi.org/10.1002/qua.560180119[Crossref]
  • [40] A.A. Makarov et al., Nuovo Cimento 52, 1061 (1967) http://dx.doi.org/10.1007/BF02755212[Crossref]
  • [41] M. Kibler, T. Negadi, Phys. Lett. A 124, 42 (1987) http://dx.doi.org/10.1016/0375-9601(87)90369-0[Crossref]
  • [42] A. Guha, S. Mukherjee, J. Math. Phys. 28, 840 (1989) http://dx.doi.org/10.1063/1.527573[Crossref]
  • [43] G. E. Draganescu, C. Campiogotto, M. Kibler, Phys. Lett. A 170, 339 (1992) http://dx.doi.org/10.1016/0375-9601(92)90883-N[Crossref]
  • [44] M. Kibler, C. Campiogotto, Phys. Lett. A 181, 1 (1993) http://dx.doi.org/10.1016/0375-9601(93)91114-K[Crossref]
  • [45] V. M. Villalba, Phys. Lett. A 193, 218 (1994) http://dx.doi.org/10.1016/0375-9601(94)90586-X[Crossref]
  • [46] Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959) http://dx.doi.org/10.1103/PhysRev.115.485[Crossref]
  • [47] P.A.M. Dirac, Proc. R. Soc. London Ser. A 133, 60 (1931) http://dx.doi.org/10.1098/rspa.1931.0130[Crossref]
  • [48] B.P. Mandal, Int. J. Mod. Phys. A 15, 1225 (2000)
  • [49] I. Sökmen, Phys. Lett. 118 A, 249 (1986)
  • [50] 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]
  • [51] B. Gönül, I. Zorba, Phys. Lett. A 269, 83 (2000) http://dx.doi.org/10.1016/S0375-9601(00)00252-8[Crossref]
  • [52] S.W. Qian, B.W. Huang, D.Y. Wang, Z.Y. Gu, Commun. Theor. Phys. 38, 139 (2002)
  • [53] G. Chen, Chin. Phys. 13, 144 (2004) http://dx.doi.org/10.1088/1009-1963/13/2/004[Crossref]
  • [54] M. Kibler, T. Negadi, Int. J. Quantum Chem. 26, 405 (1984) http://dx.doi.org/10.1002/qua.560260308[Crossref]
  • [55] M. Kibler, T. Negadi, Theor. Chim. Acta 66, 31 (1984) http://dx.doi.org/10.1007/BF00577137[Crossref]
  • [56] C.C. Gerry, Phys. Lett. A 118, 445 (1986) http://dx.doi.org/10.1016/0375-9601(86)90748-6[Crossref]
  • [57] L. Chetouani, L. Guechi, T.F. Hammann, J. Math. Phys. 33, 3410 (1992) http://dx.doi.org/10.1063/1.529889[Crossref]
  • [58] A.N. Vaidya, H. Boschi Filho, J. Math. Phys. 31, 1951 (1990) http://dx.doi.org/10.1063/1.528643[Crossref]
  • [59] M. Kibler, P. Winternitz, J. Phys. A: Math., Gen. 20, 4097 (1987) http://dx.doi.org/10.1088/0305-4470/20/13/018[Crossref]
  • [60] A. S. Zhedanov, J. Phys. A: Math, Gen. 26, 4633 (1993) http://dx.doi.org/10.1088/0305-4470/26/18/027[Crossref]
  • [61] C. Quesne, J. Phys. A: Math., Gen. 21, 3093 (1988) http://dx.doi.org/10.1088/0305-4470/21/14/010[Crossref]
  • [62] G. G. Blado, Int. J. Quantum Chem. 58, 431 (1996) http://dx.doi.org/10.1002/(SICI)1097-461X(1996)58:5<431::AID-QUA1>3.0.CO;2-Z[Crossref]
  • [63] G. G. Blado, Theo. Chim. Acta 94, 53. (1996)
  • [64] C.-Y. Chen, S.-H. Dong, Phys. Lett. A 335, 374 (2005) http://dx.doi.org/10.1016/j.physleta.2004.12.062[Crossref]
  • [65] S.M. Ikhdair, R. Sever, Int. J. Theor. Phys. 46, 2384 (2007) http://dx.doi.org/10.1007/s10773-007-9356-8[Crossref]
  • [66] A.F. Nikiforov, V. B. Uvarov, Special Functions of Mathematical Physics (Birkhauser, Bassel, 1988)
  • [67] S.M. Ikhdair, R. Sever, Int. J. Theor. Phys. 46, 1643 (2007) http://dx.doi.org/10.1007/s10773-006-9317-7[Crossref]
  • [68] S.M. Ikhdair, R. Sever, Ann. Phys. (Berlin) 16, 218 (2007) http://dx.doi.org/10.1002/andp.200610232[Crossref]
  • [69] S.M. Ikhdair, R. Sever, J. Math. Chem. 42, 461 (2007) http://dx.doi.org/10.1007/s10910-006-9115-8[Crossref]
  • [70] S.M. Ikhdair, preprint quant-ph/0605045, to appear in Int. J. Mod. Phys. E.
  • [71] C. Berkdemir, Am. J. Phys. 75, 81 (2007) http://dx.doi.org/10.1119/1.2360992[Crossref]
  • [72] Ö. Yeşiltaş, Phys. Scr. 75, 41 (2007) http://dx.doi.org/10.1088/0031-8949/75/1/006[Crossref]
  • [73] Y.-F. Cheng, T.-Q. Dai, Phys. Scr. 75, 274 (2007) http://dx.doi.org/10.1088/0031-8949/75/3/008[Crossref]
  • [74] Y.-F. Cheng, T.-Q. Dai, Chinese J. Phys. 45, 480 (2007)
  • [75] C. Berkdemir, A. Berkdemir, J. Han, Chem. Phys. Lett. 417, 326 (2006) http://dx.doi.org/10.1016/j.cplett.2005.10.039[Crossref]
  • [76] S.M. Ikhdair, R. Sever, arXiv: 0704.0573, to appear in the Cent. E. J. Phys.
  • [77] S.M. Ikhdair, preprint quant-ph/0703042, to appear in the Chinese J. Phys.
  • [78] S.M. Ikhdair, preprint quant-ph/0703008, to appear in the Int. J. Mod. Phys. C.
  • [79] S.M. Ikhdair, R. Sever, Z. Phys. C 56, 155 (1992) http://dx.doi.org/10.1007/BF01589718[Crossref]
  • [80] S.M. Ikhdair, R. Sever, Z. Phys. C 58, 153 (1993) http://dx.doi.org/10.1007/BF01554088[Crossref]
  • [81] S.M. Ikhdair, R. Sever, Z. Phys. D 28, 1 (1993) http://dx.doi.org/10.1007/BF01437449[Crossref]
  • [82] S.M. Ikhdair, R. Sever, Hadronic J. 15, 389 (1992)
  • [83] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 18, 4215 (2003) http://dx.doi.org/10.1142/S0217751X03015088[Crossref]
  • [84] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 19, 1771 (2004) http://dx.doi.org/10.1142/S0217751X0401780X[Crossref]
  • [85] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 20, 4035 (2005) http://dx.doi.org/10.1142/S0217751X05022275[Crossref]
  • [86] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 20, 6509 (2005) http://dx.doi.org/10.1142/S0217751X05021294[Crossref]
  • [87] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 21, 2191 (2006) http://dx.doi.org/10.1142/S0217751X06031636[Crossref]
  • [88] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 21, 3989 (2006) http://dx.doi.org/10.1142/S0217751X06030953[Crossref]
  • [89] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 21, 6699 (2006) http://dx.doi.org/10.1142/S0217751X06034100[Crossref]
  • [90] S.M. Ikhdair, R. Sever, preprint hep-ph/0504176, to appear in the Int. J. Mod. Phys. E.
  • [91] J.D. Louck, W.H. Shaffer, J. Mol. Spec. 4, 285 (1960) http://dx.doi.org/10.1016/0022-2852(60)90090-4[Crossref]
  • [92] J.D. Louck, J. Mol. Spec. 4, 298 (1960) http://dx.doi.org/10.1016/0022-2852(60)90091-6[Crossref]
  • [93] J.D. Louck, J. Mol. Spec. 4, 334 (1960) http://dx.doi.org/10.1016/0022-2852(60)90092-8[Crossref]
  • [94] J.D. Louck, Theory of Angular Momentum in D-Dimensional Space, Los Alamos Scientific Laboratory monograph LA-2451 (LASL, Los Alamos, 1960)
  • [95] J.D. Louck, H.W. Galbraith, Rev. Mod. Phys. 48, 69 (1976) http://dx.doi.org/10.1103/RevModPhys.48.69[Crossref]
  • [96] A. Chatterjee, Phys. Rep. 186, 249 (1990) http://dx.doi.org/10.1016/0370-1573(90)90048-7[Crossref]
  • [97] A. Erdélyi, Higher Transcendental Functions, Vol. 2 (McGraw Hill, New York, 1953)
  • [98] B.H. Bransden, C.J. Joachain, Quantum Mechanics, 2nd Ed. (Pearson Education Limited, Great Britain, 2000) 336
  • [99] S.H. Dong, Phys. Scr. 64, 273 (2001) http://dx.doi.org/10.1238/Physica.Regular.064a00273[Crossref]
  • [100] S.H. Dong, Phys. Scr. 65, 289 (2002) http://dx.doi.org/10.1238/Physica.Regular.065a00289[Crossref]
  • [101] F. Yasuk, A. Durmus, I. Boztosun, J. Math. Phys. 47, 082302 (2006) http://dx.doi.org/10.1063/1.2227258[Crossref]
  • [102] A. Durmus, F. Yasuk, J. Chem. Phys. 126, 074108 (2007) http://dx.doi.org/10.1063/1.2566432[Crossref]
  • [103] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964)
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Publication order reference
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bwmeta1.element.-psjd-doi-10_2478_s11534-008-0024-2
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