Exactly solvable potentials and the~bound-state solution of the~position-dependent mass Schr\"odinger equation in $D$-dimensional space
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 117-133
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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},
publisher = {mathdoc},
volume = {184},
number = {1},
year = {2015},
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 Schr\"odinger equation in $D$-dimensional space JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2015 SP - 117 EP - 133 VL - 184 IS - 1 PB - mathdoc 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 Schr\"odinger equation in $D$-dimensional space %J Teoretičeskaâ i matematičeskaâ fizika %D 2015 %P 117-133 %V 184 %N 1 %I mathdoc %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 Schr\"odinger 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/