Generation of exactly solvable potentials of the~$D$-dimensional position-dependent mass Schr\"odinger equation using the~transformation method
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 312-328
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We apply the extended transformation method to the constant-mass radial Schrödinger equation satisfied by a radially symmetric central potential in order to obtain exactly solvable quantum systems with a position-dependent mass in a space of arbitrary dimension in the nonrelativistic limit. The method consists of a coordinate transformation, a subsequent functional transformation, and a set of ansatzes for the mass function leading to the appearance of exactly solvable quantum systems with position-dependent masses. We also show that the Zhu–Kroemer ordering for the fitting parameter values is natural for systems with a radially symmetric mass function and a central potential. As an example, we apply the method to the Manning–Rosen potential and to the Morse potential with different choices of the mass functions. We also indicate an application of the method to the Hulthen potential.
Keywords:
position-dependent mass, exact analytic solution, Manning–Rosen potential, Morse potential, extended transformation.
@article{TMF_2015_183_2_a7,
author = {H. Rajbongshi and N. N. Singh},
title = {Generation of exactly solvable potentials of the~$D$-dimensional position-dependent mass {Schr\"odinger} equation using the~transformation method},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {312--328},
publisher = {mathdoc},
volume = {183},
number = {2},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a7/}
}
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H. Rajbongshi; N. N. Singh. Generation of exactly solvable potentials of the~$D$-dimensional position-dependent mass Schr\"odinger equation using the~transformation method. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 312-328. http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a7/