Inverse-power potentials with positive-bound energy spectrum from fractal, extended uncertainty principle and position-dependent mass arguments
Mathematics and Physics Divisions, Athens Institute for Education and Research, 8 Valaoritou Street, Kolonaki, 10671, Athens, Greece
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Accepted: 26 August 2020
Published online: 4 September 2020
In this study, we have introduced a new generalized momentum operator which takes simultaneously into account the extended uncertainty principle, the concept of position-dependent mass and fractal gradient arguments. The associated Schrödinger equation is obtained and analyzed for the case of potentials characterized by inverse-power terms with arbitrary strengths. It was observed that, in contrast to what is obtained in the literature, the corresponding quantum systems are characterized by positive-bound energy spectrum similar to what occurred in quasiparticles theory in condensed matter physics.
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