TITLE:
A New Class of Exactly Solvable Models within the Schrödinger Equation with Position Dependent Mass
AUTHORS:
Anis Dhahbi, Yassine Chargui, Adel Trablesi
KEYWORDS:
Schrödinger Equation, Position Dependent Mass, Kinetic Energy Operator, Solvable Models, Supersymmetric Quantum Mechanics, Shape Invariance
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.5,
May
6,
2019
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.