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

  • Alonso Contreras-AstorgaEmail author
  • Véronique Hussin
Part of the CRM Series in Mathematical Physics book series (CRM)


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.


Infinite square-well potential Pöschl-Teller potential Supersymmetry Point transformation Moving barrier 



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Cátedras CONACYT—Departamento de Física, CinvestavCiudad de MéxicoMexico
  2. 2.Department of PhysicsIndiana University NorthwestGaryUSA
  3. 3.Centre de Recherches Mathématiques & Departement de Mathématiques et de StatistiqueUniversité de MontréalMontréalCanada

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