Darboux integrals for Schrödinger planar vector fields via Darboux transformations

Primitivo B. Acosta-Humánez ; Chara Pantazi

Symmetry, integrability and geometry: methods and applications, Tome 8 (2012)

Résumé

In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the “invariance” of the objects of the “Darboux theory of integrability”. In particular, we also show how the shape invariance property of the potential is important in order to preserve the structure of the transformed vector field. Finally, as illustration of these results, some examples of planar vector fields coming from supersymmetric quantum mechanics are studied.

Détail

Keywords: Darboux theory of integrability, differential Galois theory, Schrödinger equation, supersymmetric quantum mechanics.
Mots-clés : Darboux transformations

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