Geodesic
Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in $D$-dimensional space
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 117-133 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We propose a transformation method using properties of classical orthogonal polynomials to construct exactly solvable potentials that provide bound-state solutions of Schrödinger equations with a position-dependent mass in $D$-dimensional space. The important feature of the method is that it favors the Zhu–Kroemer ordering of ambiguities for a radially symmetric mass function and potential. This is illustrated using hypergeometric polynomials and the associated Legendre polynomials.
Keywords: position-dependent mass, classical orthogonal polynomial, exactly solvable potential, extended transformation, Schrödinger equation. 
@article{TMF_2015_184_1_a7,
     author = {H. Rajbongshi},
     title = {Exactly solvable potentials and the~bound-state solution of the~position-dependent mass {Schr\"odinger} equation in $D$-dimensional space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {117--133},
     year = {2015},
     volume = {184},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a7/}
}
TY  - JOUR
AU  - H. Rajbongshi
TI  - Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in $D$-dimensional space
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2015
SP  - 117
EP  - 133
VL  - 184
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a7/
LA  - ru
ID  - TMF_2015_184_1_a7
ER  - 
%0 Journal Article
%A H. Rajbongshi
%T Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in $D$-dimensional space
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2015
%P 117-133
%V 184
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a7/
%G ru
%F TMF_2015_184_1_a7
H. Rajbongshi. Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in $D$-dimensional space. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 117-133. http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a7/

[1] J. C. Slater, Phys. Rev., 76:11 (1949), 1592–1601 | DOI | Zbl

[2] D. J. Ben Daneil, C. B. Duke, Phys. Rev., 152:2 (1966), 683–692 | DOI

[3] O. von Roos, Phys. Rev. B, 27:12 (1983), 7547–7552 | DOI

[4] T. Gora, F. Williams, Phys. Rev., 177:3 (1969), 1179–1182 | DOI

[5] Q.-G. Zhu, H. Kroemer, Phys. Rev. B, 27:6 (1983), 3519–3527 | DOI

[6] T. L. Li, K. J. Kuhn, Phys. Rev. B, 47:19 (1993), 12760–12770 | DOI

[7] M. R. Geller, W. Kohn, Phys. Rev. Lett., 70:20 (1993), 3103–3106 | DOI

[8] A. de Souza Dutra, C. A. S. Almeida, Phys. Lett. A, 275:1–2 (2000), 25–30, arXiv: quant-ph/0306065 | DOI | MR | Zbl

[9] A. D. Alhaidari, Phys. Rev. A, 66:4 (2002), 042116, 7 pp. | DOI

[10] A. de Souza Dutra, J. Phys. A: Math. Gen., 39:1 (2006), 203–208 | DOI | MR | Zbl

[11] O. Mustafa, S. H. Mazharimousavi, Internat. J. Theor. Phys., 46:7 (2007), 1786–1796 | DOI | MR | Zbl

[12] H. Rajbongshi, N. N. Singh, J. Modern Phys., 4:11 (2013), 1540–1545 ; Acta Phys. Polon. B, 45:8 (2014), 1701–1712 ; Х. Райбонгши, Н. Н. Сингх, ТМФ, 183:2 (2015), 312–328 | DOI | DOI | MR | DOI | MR

[13] G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructure, Les Edition de Physique, Paris, 1988

[14] P. Harrison, Quantum Wells, Wires and Dots. Theoretical and Computational Physics, John Wiley Sons, New York, 2000

[15] L. Serra, E. Lipparini, Europhys. Lett., 40:6 (1997), 667–672 | DOI

[16] F. A. de Saavedra, J. Boronat, A. Polls, A. Fabrocini, Phys. Rev. B, 50:6 (1994), 4248–4251, arXiv: cond-mat/9403075 | DOI | MR

[17] P. Ring, P. Schuck, The Nuclear Many-Body Problem, Springer, Berlin, 1980 | MR

[18] B. Gönül, O. Özer, B. Gönül, F. Üzgün, Modern Phys. Lett. A, 17:37 (2002), 2453–2465, arXiv: quant-ph/0211113 | DOI | MR | Zbl

[19] C. Tazcan, R. Sever, J. Math. Chem., 42:3 (2007), 387–395 | DOI | MR

[20] C. Quesne, SIGMA, 5 (2009), 046, 17 pp. | DOI | MR | Zbl

[21] H. Panahi, Z. Bakhshi, Acta Phys. Polon. B, 41:1 (2010), 11–21

[22] M. Jafarpour, B. Ashtari, Adv. Stud. Theor. Phys., 5:1–4 (2011), 131–142 | MR | Zbl

[23] R. Sever, C. Tezcan, Ö. Yeşiltaş, M. Bucurgat, Internat. J. Theor. Phys., 47:9 (2008), 2243–2248 | DOI | MR | Zbl

[24] C. Tezcan, R. Sever, Ö. Yeşiltaş, Internat. J. Theor. Phys., 47:6 (2008), 1713–1721 | DOI | MR | Zbl

[25] S. Meyur, Bulg. J. Phys., 38:4 (2011), 357–363 | MR

[26] R. Koç, H. Tütüncüler, Ann. Phys. (8), 12:11–12 (2003), 684–691 | DOI | MR | Zbl

[27] C. Quesne, B. Bagchi, A. Banergee, V. M. Tkachuk, Bulg. J. Phys., 33:4 (2006), 308–318 | MR | Zbl

[28] C. Quesne, SIGMA, 3 (2007), 067, 14 pp. | DOI | MR | Zbl

[29] P. K. Jha, H. Eleuch, Y. V. Rostovtsev, J. Modern Opt., 58:8 (2011), 652–656, arXiv: 1010.1744 | DOI | MR

[30] J. Yu, S.-H. Dong, G.-H. Sun, Phys. Lett. A, 322:5–6 (2004), 290–297 | DOI | MR | Zbl

[31] A. Schulze-Halberg, Internat. J. Modern Phys. A, 22:8–9 (2007), 1735–1769 | DOI | MR | Zbl

[32] A. Schulze-Halberg, Internat. J. Modern Phys. A, 23:3–4 (2008), 537–546 | DOI | MR | Zbl

[33] C. Quesne, Ann. Phys. (N. Y.), 321:5 (2006), 1221–1239, arXiv: quant-ph/0508216 | DOI | MR | Zbl

[34] A. G. M. Schmidt, Phys. Lett. A, 353:6 (2006), 459–462 | DOI

[35] D. A. Kulikov, V. M. Shapoval, $\hbar$-Expansion for the Schrödinger equation with a position-dependent mass, arXiv: 1206.1666 | MR

[36] S. A. S. Ahmed, Internat. J. Theor. Phys., 36:8 (1997), 1893–1905 ; N. Saikia, Turk. J. Phys., 36:2 (2012), 187–196 ; Н. Саикиа, С. А. С. Ахмед, ТМФ, 168:2 (2011), 291–298 ; S. A. S. Ahmed, B. C. Borah, D. Sharma, Eur. Phys. J. D, 17:1 (2001), 5–11 ; S. A. S. Ahmed, L. Buragohain, Phys. Scr., 80:2 (2009), 025004, 6 pp. ; S. A. S. Ahmed, L. Buragohain, Eur. J. Theor. Phys., 7:23 (2010), 145–154; N. Bhagawati, N. Saikia, N. N. Singh, Acta Phys. Polon. B, 44:8 (2013), 1711–1723, arXiv: ; N. Bhagawati, Acta Phys. Polon. B, 45:1 (2014), 15–28, arXiv: ; A. Bharali, Phys. Scr., 88:3 (2013), 035009, 7 pp. 1309.31521402.1265 | DOI | MR | Zbl | DOI | MR | DOI | DOI | MR | Zbl | DOI | DOI | Zbl | DOI | MR | DOI | MR | DOI | Zbl

[37] S. A. S. Ahmed, B. C. Borah, J. Phys. A: Math. Gen., 36:39 (2003), 10071–10082 | DOI | MR | Zbl