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On the Construction of Position-Dependent Mass Models with Quadratic Spectra

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Geometric Methods in Physics XXXIX (WGMP 2022)

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Abstract

The construction of position-dependent mass Hamiltonian hierarchies is considered in the factorization context. It is shown that the superpotentials, the deformed potentials, and their bound state wave functions can be expressed in terms of a transformation function u that satisfy a second-order linear equation. The connection of this equation with a family of Ermakov equations allows the generation of different types of position-dependent mass models with quadratic spectra.

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Acknowledgements

This research has been funded by Consejo Nacional de Ciencia y Tecnología (CONACyT), Mexico, Grant Numbers A1-S-24569 and CF19-304307, and Instituto Politécnico Nacional (IPN), Mexico Grant SIP20221346. M A Medina-Armendariz acknowledges the support of CONACyT through the scholarship 001624.

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Authors and Affiliations

  1. Instituto Politécnico Nacional, UPIITA, Av. Instituto Politécnico Nacional 2580, Ciudad de México, Mexico

    Sara CruzyCruz

  2. Instituto Politécnico Nacional, Laboratorio de Ciencias de la Información Cuántica, CIC, Ciudad de México, Mexico

    Miguel A. Medina-Armendariz

Authors
  1. Sara CruzyCruz
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  2. Miguel A. Medina-Armendariz
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Correspondence to Sara CruzyCruz .

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Editors and Affiliations

  1. Departamento de Física, CINVESTAV, Ciudad de México, Mexico

    Piotr Kielanowski

  2. Faculty of Mathematics, University of Białystok, Białystok, Poland

    Alina Dobrogowska

  3. Departments of Mathematics, Physics, Learning & Teaching, Rutgers University, New Brunswick, NJ, USA

    Gerald A. Goldin

  4. Faculty of Mathematics, University of Białystok, Białystok, Poland

    Tomasz Goliński

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CruzyCruz, S., Medina-Armendariz, M.A. (2023). On the Construction of Position-Dependent Mass Models with Quadratic Spectra. In: Kielanowski, P., Dobrogowska, A., Goldin, G.A., Goliński, T. (eds) Geometric Methods in Physics XXXIX. WGMP 2022. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-30284-8_8

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