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Infinite Square-Well, Trigonometric Pöschl-Teller and Other Potential Wells with a Moving Barrier

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Integrability, Supersymmetry and Coherent States

Part of the book series: CRM Series in Mathematical Physics ((CRM))

Abstract

Using mainly two techniques, a point transformation and a time dependent supersymmetry, we construct in sequence several quantum infinite potential wells with a moving barrier. We depart from the well-known system of a one-dimensional particle in a box. With a point transformation, an infinite square-well potential with a moving barrier is generated. Using time dependent supersymmetry, the latter leads to a trigonometric Pöschl-Teller potential with a moving barrier. Finally, a confluent time dependent supersymmetry transformation is implemented to generate new infinite potential wells, all of them with a moving barrier. For all systems, solutions of the corresponding time dependent Schrödinger equation fulfilling boundary conditions are presented in a closed form.

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Acknowledgements

This work has been supported in part by research grants from Natural sciences and engineering research council of Canada (NSERC). ACA would like to thank the Centre de Recherches Mathématiques for kind hospitality.

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Authors and Affiliations

  1. Cátedras CONACYT—Departamento de Física, Cinvestav, Ciudad de México, Mexico

    Alonso Contreras-Astorga

  2. Department of Physics, Indiana University Northwest, Gary, IN, USA

    Alonso Contreras-Astorga

  3. Centre de Recherches Mathématiques & Departement de Mathématiques et de Statistique, Université de Montréal, Montréal, QC, Canada

    Véronique Hussin

Authors
  1. Alonso Contreras-Astorga
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  2. Véronique Hussin
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Corresponding author

Correspondence to Alonso Contreras-Astorga .

Editor information

Editors and Affiliations

  1. Department of Physics, Ankara University, Ankara, Turkey

    Şengül Kuru

  2. Department of Theoretical Physics, Atomic Physics and Optics, University of Valladolid, Valladolid, Spain

    Javier Negro

  3. Department of Theoretical Physics, Atomic Physics and Optics, University of Valladolid, Valladolid, Spain

    Luis M. Nieto

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Contreras-Astorga, A., Hussin, V. (2019). Infinite Square-Well, Trigonometric Pöschl-Teller and Other Potential Wells with a Moving Barrier. In: Kuru, Ş., Negro, J., Nieto, L. (eds) Integrability, Supersymmetry and Coherent States. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-20087-9_11

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