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arXiv · 1911.05023

The nonlocal Darboux transformation of the stationary axially symmetric Schr\"odinger equation and generalized Moutard transformation

Andrey Kudryavtsev
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Abstract

The nonlocal Darboux transformation of the stationary axially symmetric Schr\"odinger equation is considered. It is shown that a special case of the nonlocal Darboux transformation provides the generalization of the Moutard transformation. Formulae for the generalized Moutard transformation are obtained. New examples of two - dimensional potencials and exact solutions for the stationary axially symmetric Schr\"odinger equation are obtained as an application of the generalized Moutard transformation.

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Andrey Kudryavtsev. 2019-11-12. The nonlocal Darboux transformation of the stationary axially symmetric Schr\"odinger equation and generalized Moutard transformation. https://arxiv.org/abs/1911.05023

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