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arXiv · quant-ph/0311139

New solvable quantum mechanical potentials by iteration of the free V=0 potential

Pedro Blecua·Luis J. Boya·Antonio Segui
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Abstract

A huge family of solvable potentials can be generated by systematically exploiting the factorization (Darboux) method. Starting from the free case, a large class of the known solvable families is thus reproduced, together with new ones. We explicitly find and solve several new singular potentials obtained by iteration from the V=0 case; some of them have an E=0 bound state and constant phase shift without being explicitly scale invariant. The new potentials are rational functions, and can be related to rational solutions of the KdV family.

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Pedro Blecua, Luis J. Boya, Antonio Segui. 2003-11-20. New solvable quantum mechanical potentials by iteration of the free V=0 potential. https://doi.org/10.1393/ncb%2Fi2002-10008-y

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