Infinite square-well, trigonometric P\"oschl-Teller and other potential wells with a moving barrier
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.
Keywords
Cite
@article{arxiv.1901.04606,
title = {Infinite square-well, trigonometric P\"oschl-Teller and other potential wells with a moving barrier},
author = {Alonso Contreras-Astorga and Véronique Hussin},
journal= {arXiv preprint arXiv:1901.04606},
year = {2019}
}