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Infinite square-well, trigonometric Pöschl-Teller and other potential wells with a moving barrier. (English) Zbl 1425.81027

Kuru, Şengül (ed.) et al., Integrability, supersymmetry and coherent states. A volume in honour of Professor Véronique Hussin. In part selected contributions from the 6th international workshop on new challenges in quantum mechanics: integrability and supersymmetry, Valladolid, Spain, June 27–30, 2017. Cham: Springer. CRM Ser. Math. Phys., 285-299 (2019).
Summary: 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.
For the entire collection see [Zbl 1421.81004].

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q41 Time-dependent Schrödinger equations and Dirac equations
81Q60 Supersymmetry and quantum mechanics
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