×

Exact solutions of the Schrödinger equation with position-dependent effective mass via general point canonical transformation. (English) Zbl 1132.81354

Summary: Exact solutions of the Schrödinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transformation is introduced by using a free parameter. Two different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.

MSC:

81V55 Molecular physics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] G. Bastard, Wave Mechanics Applied to Heterostructure (Les Ulis, Les Edition de Physique, 1989).
[2] P. Harrison, Quantum Wells, Wires and Dots (New York, 2000), L. Serra and E. Lipparin, Europhys. Lett. 40 (1997) 667.
[3] Barranco M., Pi M., Gatica S.M., Hernandez E.S., Navarro J. (1997). Phys. Rev. B56:8997
[4] Arias de Saavedra F., Boronat J., Poll A., Fabrocini A. (1997). Phys. Rev. B50:4248
[5] C. Weisbuch and B. Vinter, Quantum Semiconductor Heterostructure (New York, Academic Press, 1993) and references therein; O. Von Roos, Phys. Rev. B27 (1983) 7547; O. Von Roos and H. Mavromatis, Phys. Rev. B31 (1985) 2294; R.A. Morrow, Phys. Rev. B35 (1987) 8074; V. Trzeciakowski, Phys. Rev. B38 (1988) 4322; I. Galbraith and G. Duygan, Phys. Rev. B38 (1988) 10057; K. Young, Phys. Rev. B39 (1989) 13434; G.T. Einvoll, P.C. Hemmer and J. Thomsen, Phys. Rev. B42 (1990), 3485; G. T. Einvoll, Phys. Rev. B42 (1990) 3497.
[6] Yu J., Dong S.H., Sun G.H. (1999). Phys. Lett. A322:290
[7] Dong S.H., Lozada-Cassou M. (2005). Phys. Lett. 337:313 · Zbl 1136.81353
[8] A.D. Alhaidari, Phys. Rev. A66 042116; A.D. Alhaidari, Int. J. Theor. Phys. 42 (2003) 2999.
[9] Gönül B., Özer O., Gönül B., Üzgün F. (2002). Mod. Phys. Lett. A1:2453
[10] Yu J., Dong J. (2004). J. Phys. Lett. A325:194
[11] Chen G., Chen Z.D. (2004). Phys. Lett. A331:312
[12] Bencheikh K., Berkane S., Bouizane S. (2004). J. Phys. A: Math. Gen. 37:10719 · Zbl 1064.81043
[13] Jiang L., Yi L., Jia L.C.S. (2005). Phys. Lett. A345:279
[14] L. Dekar, T. Chetouani and F. Hammann, J. Phys. A: Math. Gen. 39 (1998) 2551; L. Dekar, T. Chetouani and F. Hammann, Phys. Rev. A59 (1999) 107.
[15] Plastino A.R., Rigo A., Casas M., Plastino A. (1999). Phys. Rev. A60:4318
[16] Milanović V., Ikonić Z. (1999). J. Phys. A: Math. Gen. 32:7001 · Zbl 0966.81022
[17] de S. Dutra and C.A.S. Almeida Phys. Lett. A275 (2000) 25; A. de S. Dutra, M.B. Hott and C.A.S. Almeida, Europhys. Lett. 62 (2003) 8.
[18] R. Koc, M. Koca, and E. Körcük, Eur. J. Phys. A: Math. Gen. 35, (2002), L527; R. Koc and M. Koca, J. Phys. A: Math. Gen. 36 (2003) 8105.
[19] B. Roy and P. Roy, J. Phys. A: Math. Gen. 36, (2003) 8105; B. Roy and P. Roy, Phys. Lett. A340, (2005) 70.
[20] Quesne C., Tkachuk V.M. (2004). J. Phys. A: Math. Gen 37:4267 · Zbl 1063.81070
[21] Ou Y.C., Cao Z.Q., Shen Q.H. (2004). J. Phys. A: Math. Gen. 37:4283 · Zbl 1052.81031
[22] B. Bagchi, P. Gorain, C. Quesne and R. Roychoudhury, Mod. Phys. Lett. A19, (2004) 2765; B. Bagchi, P. Gorain, C. Quesne and R. Roychoudhury, Czech. J. Phys. 54 (2004) 1019; B. Bagchi, C. Quesne and V.M. Tkachul, J. Phys. A: Math. Gen. 38 (2004) 2929. · Zbl 1065.81039
[23] Chen Z.D., Chen G. (2005). Physica Scripta 72:11 · Zbl 1078.82541
[24] De R., Dutt R., Sukhatme U. (1992). J. Phys. A: Math. Gen. 25:L843
[25] Dutt R., Khare A., Varshni Y.P. (1995). J. Phys. A: Math. Gen. 28:L107 · Zbl 0851.34080
[26] Kocak M., Zorba I., Gönül B. (2002). Mod. Phys. Lett A16:2127
[27] C.S. Jia, Y.F. Diao, M. Li, Q.B. Yang, L.T. Sun and R.Y. Huang, J. Phys. A: Math. Gen. 37 (2004) 11275.
[28] Egrifes H., Demirhan D., Büyükkilic F. (1989). Phys. Scr. 60:195 · Zbl 0943.81009
[29] C.S. Jia and Y. Li, J. Phys. A: Math. Gen. 28, 2004, L107; J.Y. Liu and L.T. Sun, Phys. Lett. A331 (2003) 115.
[30] Egrifes H., Demirhan D., Büyükkilic F. (2000). Phys. Lett. A275:229 · Zbl 1115.81332
[31] Arai A. (1991). J. Math. Anal. Appl. 158:63 · Zbl 0731.47055
[32] de A., Dutra S. (2005). Phys. Lett. A339:252
[33] Li L.Z., Diao Y.F., Liu J.Y., Jia C.S. (2004). Phys. Lett. A333:212
[34] Zhang X.C., Liu Q.W., Jia C.S., Wang L.Z. (2005). Phys. Lett. A340:59
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.