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Inverse-power potentials with positive-bound energy spectrum from fractal, extended uncertainty principle and position-dependent mass arguments

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Abstract

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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The author would like to thank the kind referee for the invaluable and positive suggestions, which improved the manuscript.

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  1. Mathematics and Physics Divisions, Athens Institute for Education and Research, 8 Valaoritou Street, Kolonaki, 10671, Athens, Greece

    Rami Ahmad El-Nabulsi

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El-Nabulsi, R.A. Inverse-power potentials with positive-bound energy spectrum from fractal, extended uncertainty principle and position-dependent mass arguments. Eur. Phys. J. Plus 135, 693 (2020). https://doi.org/10.1140/epjp/s13360-020-00717-w

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