Abstract
The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics. In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum. To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition. Recent outcomes of non-Hermitian quantum mechanics are also taken into account.
Highlights
The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics
In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum
To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition
Summary
While the interest in searching exactly solvable quantum PDM systems is still increasing [25, 36], the most interesting question remains how to order the mass operator with respect to the momentum operator when it comes to building the KEO of the Hamiltonian. The Hermiticity condition of the Hamiltonian, seems to be inadequate to definitely specify a unique form for the Kinetic Energy Operator (KEO) with a position-dependent effective mass. Such a dilemma brings us back to rethink about the general rule has to be followed in associating operators in quantum-mechanical with respect to the classical quantities
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