The study of physical systems endowed with a position-dependent\nmass (PDM) remains a fundamental issue of quantum mechanics.\nIn this paper we use a new approach, recently developed by us\nfor building the quantum kinetic energy operator (KEO) within\nthe Schrodinger equation, in order to construct a new class of exactly\nsolvable models with a position varying mass, presenting a\nharmonic-oscillator-like spectrum. To do so we utilize the formalism\nof supersymmetric quantum mechanics (SUSY QM) along with\nthe shape invariance condition. Recent outcomes of non-Hermitian\nquantum mechanics are also taken into account.
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