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Supersymmetric Quantum Mechanics and Painlevé IV Transcendents

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Geometric Methods in Physics XXXIX (WGMP 2022)

Part of the book series: Trends in Mathematics ((TM))

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Abstract

A brief overview of supersymmetric quantum mechanics is made, which is illustrated by the harmonic oscillator potential. The polynomial Heisenberg algebras are studied, as well as the realizations supplied by the supersymmetric partners of the harmonic oscillator. The general systems ruled by second-degree polynomial Heisenberg algebras are explored, together with its link with the Painlevé IV equation. An algorithm for generating Painlevé IV transcendents is discussed.

To the memory of my PhD adviser and dear friend Bogdan Mielnik

The author acknowledges the support of CONACYT (Mexico), project FORDECYT-PRONACES/61533/2020.

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Authors and Affiliations

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

    David J. Fernández C.

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  1. David J. Fernández C.
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Correspondence to David J. Fernández C. .

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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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C., D.J.F. (2023). Supersymmetric Quantum Mechanics and Painlevé IV Transcendents. 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_27

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