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Darboux integrals for Schrödinger planar vector fields via Darboux transformations
Acosta Humánez, Primitivo Belén; Pantazi, Chara
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Àrees temàtiques de la UPC::Física::Mecànica quàntica
Quantum physics
Mecànica quàntica
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