Shape-invariant quantum Hamiltonian with position-dependent effective mass through second-order supersymmetry

Abstract

Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner Hamiltonians may be exploited to obtain a simple shape-invariant condition. Indeed a novel relation between potential and mass functions is derived, which leads to a class of exactly solvable model. As an illustration of our procedure, two examples are given for which one obtains whole spectra algebraically. Both shape-invariant potentials exhibit harmonic-oscillator-like or singular-oscillator-like spectra depending on the values of the shapeinvariant parameter.

A General type of Liénard Second Order Differential Equation: Classical and Quantum Mechanical Study

“…(12) . Further, we find an extensive study on the position dependence of mass pertaining to various aspects have been carried out by several authors (von Roos, 1983;Quesne and Tkachuk, 2004;Koç and Tütüncüler, 2003;Dutra et al, 2003;Bagchi et al, 2006;Ganguly et al, 2006;Ganguly and Nieto, 2007;Lévai and Özer, 2010;Killingbeck, 2011;Mazharimousavi, 2012;Yahiaoui and Bentaiba, 2012;Mustafa, 2015;Rajbongshi and Singh, 2015). In the present case, we study the discrete nature of spectra and its stability for the newly generated Hamiltonian (Eqn.…”

$\mathcal {CPT}$ CPT -conserved effective mass Hamiltonians through first and higher order charge operator $\mathcal {C}$C in a supersymmetric framework

“…Finally, in the context of the N -th order SUSY, a mass-deformed superpotential W m (x) can be introduced which is given by the form [28] …”

A complete set of eigenstates for position-dependent massive particles in a Morse-like scenario

“…Moreover, some time ago, it was discussed in the literature the exact solvability of some classes of one-dimensional Hamiltonians, where the potentials has a PDM, with ordering ambiguity [29], after that, a large number of works regarding one-dimensional Hamiltonians with ordering ambiguity has emerged in the scientific community along the last few years [30][31][32][33][34][35][36]. Another interesting research line regards to the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence .…”