Generation of isospectral combinations of the potential and the effective-mass variations by supersymmetric quantum mechanics

Solutions of the nonrelativistic wave equation with position-dependent effective mass

“…Recently, several contributions have emerged in the literature where some of the above-mentioned developments in nonrelativistic quantum mechanics were extended to the case of spatially dependent mass distribution [10][11][12][13][14]. The motivation for obtaining exact solutions of the wave equation with position dependent mass comes from the wide range of applications of these solutions in various areas of material science and condensed matter.…”

“…Shape invariance was also addressed in this setting and the energy spectra were obtained algebraically for several examples. Coordinate transformation in supersymmetric quantum mechanics were used in [12] to generate isospectral potentials with position dependent mass. The ordering ambiguity of the mass and momentum operator and its effect on the exact solutions was addressed in [13] where several examples are considered.…”

-fold supersymmetry in quantum systems with position-dependent mass

“…For references, see e.g., Refs. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] and those cited therein. Due to the fact that the position-dependent mass m(q) does not commute with the momentum operator p = −id/dq, ambiguity arises in defining a quantum kinetic operator which is formally Hermitian and reduces to the classical kinetic term T = p 2 /2m(q).…”

A squeeze-like operator approach to position-dependent mass in quantum mechanics

“…Among them, one may mention the Morse and Coulomb potentials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Moreover, it has been recently shown [19] that to lowest order of perturbation theory, there exists a whole class of Hermitian position-dependent-mass Hamiltonians that are associated with pseudo-Hermitian Hamiltonians.…”