Darboux Integrals for Schrödinger planar vector fields via Darboux transformations
Acosta-Humánez, Primitivo B. (Universidad del Norte (Colombia). Departamento de Matemáticas y Estadística)
Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)

Date:	2012
Abstract:	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 elements 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. Free particle, square well, harmonic oscillator, three dimensional harmonic oscillator and Coulomb potential, are presented as natural examples coming from supersymmetric quantum mechanics.
Grants:	Ministerio de Ciencia e Innovación MTM2009-06973 Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-859
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Darboux theory of integrability ; Darboux transformations ; Differential Galois theory ; Schrödinger equation ; Supersymmetric Quantum Mechanics
Published in:	SIGMA. Symmetry, Integrability and Geometry. Methods and Applications, Vol. 8 (2012) , p. 26 pages, ISSN 1815-0659

Postprint 38 p, 776.1 KB

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