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arXiv · 1901.04606

Infinite square-well, trigonometric P\"oschl-Teller and other potential wells with a moving barrier

Alonso Contreras-Astorga·Véronique Hussin
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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 P\"oschl-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 Schr\"odinger equation fulfilling boundary conditions are presented in a closed form.

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Alonso Contreras-Astorga, Véronique Hussin. 2019-01-14. Infinite square-well, trigonometric P\"oschl-Teller and other potential wells with a moving barrier. https://doi.org/10.1007/978-3-030-20087-9_11

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