×

A general approach for the exact solution of the Schrödinger equation. (English) Zbl 1162.81369

Summary: The Schrödinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schrödinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U15 Exactly and quasi-solvable systems arising in quantum theory
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] Chatterjee, A.: Phys. Rep. 186, 249 (1990)
[2] Cooper, F., Khare, A., Sukhatme, U.: Phys. Rep. 251, 267 (1995)
[3] Roy, B.: Phys. Rev. A 34, 5108 (1986)
[4] Panja, M.M., Dutt, R., Varshni, Y.P.: Phys. Rev. A 42, 106 (1990)
[5] Chatterjee, A.: Phys. Rev. A 35, 2722 (1987)
[6] Sever, R., Tezcan, C.: Phys. Rev. A 35, 2725 (1987)
[7] Sever, R., Tezcan, C.: Phys. Rev. A 36, 1045 (1987)
[8] Egrifes, H., Demirhan, D., Büyükkilic, F.: Phys. Lett. A 275, 229 (2000) · Zbl 1115.81332
[9] Ikhdair, S.M., Sever, R.: J. Mol. Struct. Theochem 806, 155 (2007)
[10] Dong, S.H., Chen, C.Y., Lozada-Casson, M.: J. Phys. B 38, 2211 (2005)
[11] Dong, S.H., Morales, D., Garcia-Ravelo, J.: Int. J. Mod. Phys. E 16, 189 (2007)
[12] Qiang, W.-C., Dong, S.-H.: Phys. Lett. A 363, 169 (2007) · Zbl 1197.81128
[13] Ikhdair, S.M., Sever, R.: Int. J. Theor. Phys. 46, 2384 (2007) · Zbl 1133.81017
[14] Ikhdair, S.M., Sever, R.: Int. J. Theor. Phys. 46, 1643 (2007) · Zbl 1118.81024
[15] Ikhdair, S.M., Sever, R.: Ann. Phys. Leipz. 16, 10232 (2007) · Zbl 1114.81029
[16] Ikhdair, S.M., Sever, R.: J. Math. Chem. 41, 329 (2007) · Zbl 1127.81010
[17] Ikhdair, S.M., Sever, R.: J. Math. Chem. 42, 462 (2007) · Zbl 1132.81352
[18] Ikhdair, S.M., Sever, R.: Int. J. Mod. Phys. A 21, 6465 (2006) · Zbl 1111.81356
[19] Hall, R.L., Saad, N.: J. Chem. Phys. 109, 2983 (1998)
[20] Setare, M.R., Karimi, E.: Phys. Scr. 75, 90 (2007) · Zbl 1118.81538
[21] Ikhdair, S.M., Sever, R.: Z. Phys. C 56, 155 (1992)
[22] Ikhdair, S.M., Sever, R.: Z. Phys. C 58, 153 (1993)
[23] Ikhdair, S.M., Sever, R.: Z. Phys. D 28, 1 (1993)
[24] Ikhdair, S.M., Sever, R.: Int. J. Mod. Phys. A 18, 4215 (2003) · Zbl 1034.81532
[25] Ikhdair, S.M., Sever, R.: Int. J. Mod. Phys. A 19, 1771 (2004)
[26] Ikhdair, S.M., Sever, R.: Int. J. Mod. Phys. A 20, 4035 (2005)
[27] Ikhdair, S.M., Sever, R.: Int. J. Mod. Phys. A 20, 6509 (2005) · Zbl 1077.81533
[28] Ikhdair, S.M., Sever, R.: Int. J. Mod. Phys. A 21, 2191 (2006) · Zbl 1102.81318
[29] Ikhdair, S.M., Sever, R.: Int. J. Mod. Phys. A 21, 3989 (2006) · Zbl 1102.81318
[30] Ikhdair, S.M., Sever, R.: Int. J. Mod. Phys. A 21, 6699 (2006) · Zbl 1110.81160
[31] Özçelik, S., Şimşek, M.: Phys. Lett. A 152, 145 (1991)
[32] Dong, S.-H.: Phys. Scr. 64, 273 (2001) · Zbl 1061.81511
[33] Dong, S.-H.: Phys. Scr. 65, 289 (2002) · Zbl 1061.81509
[34] Berkdemir, C., Berkdemir, A., Han, J.: Chem. Phys. Lett. 417, 326 (2006)
[35] Aktaş, M., Sever, R.: Mod. Phys. Lett. A 19, 2871 (2004) · Zbl 1061.81030
[36] Filho, E.D., Ricotta, R.M.: Phys. Lett. A 269, 269 (2000) · Zbl 1115.81348
[37] Bagchi, B., Quesne, C.: Phys. Lett. A 300, 18 (2002) · Zbl 0997.81036
[38] Bagchi, B., Cannata, F., Quesne, C.: Phys. Lett. A 269, 79 (2000) · Zbl 1115.81392
[39] Faridfathi, G., Sever, R., Aktaş, M.: J. Math. Chem. 38, 533 (2005) · Zbl 1100.81028
[40] Nikiforov, A.F., Uvarov, V.B.: Special Functions of Mathematical Physics. Birkhäuser, Basel (1988) · Zbl 0624.33001
[41] Morse, P.M.: Phys. Rev. 34, 57 (1929) · JFM 55.0539.02
[42] Egrifes, H., Demirhan, D., Büyükkilic, F.: Phys. Scr. A 60, 195 (1989) · Zbl 0943.81009
[43] Jia, C.S., Sun, Y., Li, Y.: Phys. Lett. A 331, 115 (2003) · Zbl 1059.81046
[44] Tezcan, C., Sever, R.: J. Math. Chem. 42, 387 (2006) · Zbl 1132.81354
[45] Ikhdair, S., Sever, R.: J. Mol. Struct. Theochem 806, 155 (2007)
[46] Sever, R., Tezcan, C., Aktaş, M., Yeşiltaş, Ö.: J. Math. Chem. 43, 845 (2007) · Zbl 1151.81333
[47] Goldman, I.I., Krivchenkov, V.D.: Problems in Quantum Mechanics. Pergamon Press, New York (1961) · Zbl 0094.23407
[48] Weissman, Y., Jortner, J.: Phys. Lett. A 70, 177 (1979)
[49] Szego, M.L.: Chem. Phys. 87, 431 (1984)
[50] Sato, M., Goodisman, J.: Am. J. Phys. 53, 350 (1985)
[51] Erkoç, Ş, Sever, R.: Phys. Rev. A 37, 2687 (1988)
[52] Sever, R., Bucurgat, M., Tezcan, C., Yeşiltaş, Ö.: J. Math. Chem. 43, 749 (2007) · Zbl 1196.81115
[53] Mie, G.: Ann. Phys. Leipz. II, 657 (1903) · JFM 34.0983.01
[54] Maitland, G.C., Rigby, M., Smith, E.B., Wakeham, W.A.: Intermolecular Forces. Oxford Univ. Press, Oxford (1987)
[55] Berkdemir, C., Berkdemir, A., Sever, R.: J. Math. Chem. 43, 944 (2008) · Zbl 1154.81377
[56] Gonul, B., Koksal, K.: Phys. Scr. 76, 565 (2007) · Zbl 1129.81319
[57] Ikhdair, S.M., Sever, R.: Int. J. Theor. Phys. 46, 1643 (2007) · Zbl 1118.81024
[58] Berkdemir, C., Berkdemir, A., Sever, R.: Mod. Phys. Lett. A 21, 208 (2006) · Zbl 1126.81023
[59] Fakhri, H., Sadeghi, J.: Mod. Phys. Lett. A 19, 615 (2004) · Zbl 1080.81650
[60] Costa, L.S., et al.: J. Phys. B At. Mol. Opt. Phys. 32, 2461 (1999)
[61] Egrifes, H., Demirhan, D., Büyükkilic, F.: Phys. Scr. 59, 90 (1999) · Zbl 1063.81532
[62] Pöschl, G., Teller, E.: Z. Phys. 83, 143 (1933)
[63] Dong, S.H., Qiang, W.C., Garcia-Ravelo, J.: Int. J. Mod. Phys. A 23, 1537 (2008) · Zbl 1153.81485
[64] Dutt, R., Khare, A., Varshni, Y.P.: J. Phys. A Math. Gen. 28, L107 (2004) · Zbl 0851.34080
[65] Jia, C.S., Li, Y.: Phys. Lett. A 305, 231 (2002) · Zbl 1001.81018
[66] Simsek, M., Yalcin, Z.: J. Math. Chem. 16, 211 (1994)
[67] Kratzer, A.: Z. Phys. 3, 289 (1920)
[68] Fues, E.: Ann. Phys. 80, 367 (1926) · JFM 52.0968.07
[69] Makarov, A.A., et al.: Nuovo Cim. 52, 106 (1967)
[70] Ikhdair, S., Sever, R.: Int. J. Theor. Phys. 46, 2384 (2007). ArXiv:quant-ph/0702186 · Zbl 1133.81017
[71] Khare, A., Bhaduri, R.K.: Am. J. Phys. 62, 1008 (1994)
[72] Cooper, F., Khare, A.A., Sukhatme, U.: Phys. Rep. 251, 267 (2007)
[73] Dong, S.H., Chen, C.Y., Cassou, M.L.: Int. J. Quant. Chem. 105, 453 (2005)
[74] Kocak, M., Zorba, I., Gonul, B.: Mod. Phys. Lett. A 17, 2127 (2002) · Zbl 1083.81601
[75] Gonul, B., Zorba, I.: Phys. Lett. A 269, 83 (2000) · Zbl 1115.81394
[76] Mandal, B.: Am. J. Phys. A 15, 1225 (2000)
[77] Gerry, C.C.: Phys. Lett. A 118, 445 (1986)
[78] Dutt, R., Gangopadhaya, A., Sukhatme, U.P.: Am. J. Phys. 65, 400 (1997)
[79] Chetouani, L., Guechi, L.: J. Math. Phys. 33, 3410 (1992) · Zbl 0787.22023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.