Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 14 Jul 2012Embargo end date: 01 Jan 2011 Spain Publisher:SIGMA (Symmetry, Integrability and Geometry: Methods and Application)Journal:Symmetry, Integrability and Geometry: Methods and Applications (eissn: 1815-0659,

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Authors: Acosta Humánez, Primitivo Belén; Pantazi, Chara;

doi: 10.3842/sigma.2012.043 , 10.48550/arxiv.1111.0120

arXiv: 1111.0120

handle: 2117/16689

Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations

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Abstract

In this paper we study the Darboux transformations of planar vector fields of Schr��dinger 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.

Country

Spain

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
Autonomous University of Barcelona
Spain
Universidad del Norte
Colombia
Universitat Politècnica de Catalunya
Spain

Keywords

Differential equations, :12 Field theory and polynomials::12H Differential and difference algebra [Classificació AMS], :Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis [Àrees temàtiques de la UPC], :34 Ordinary differential equations::34C Qualitative theory [Classificació AMS], Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, Linear ordinary differential equations and systems, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis, Supersymmetric quantum mechanics, FOS: Physical sciences, Schrödinger equation, Equacions diferencials, Differential Galois theory, Differential algebra, Polynomials, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions diferencials ordinàries, :Matemàtiques i estadística::Equacions diferencials i integrals::Equacions diferencials ordinàries [Àrees temàtiques de la UPC], :81 Quantum theory::81Q General mathematical topics and methods in quantum theory [Classificació AMS], differential Galois theory, Darboux transformations, QA1-939, :34 Ordinary differential equations::34A General theory [Classificació AMS], 12H05 (Primary) 34A30, 34C14, 81Q60, 32S65 (Secondary), Mathematical Physics, supersymmetric quantum mechanics, Quantum Physics, Classificació AMS::81 Quantum theory::81Q General mathematical topics and methods in quantum theory, Mathematical Physics (math-ph), Supersymmetric Quantum Mechanics, Darboux theory of integrability, Polinomis, Classificació AMS::34 Ordinary differential equations::34A General theory, Symmetries, invariants of ordinary differential equations, Classificació AMS::12 Field theory and polynomials::12H Differential and difference algebra, Quantum Physics (quant-ph), Mathematics

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