1111.0120 (Primitivo B. Acosta-Humánez et al.)

Darboux Integrals for Schrödinger Planar Vector Fields via Darboux
Transformations    [PDF]

Primitivo B. Acosta-Humánez, Chara Pantazi

In this paper we study the Darboux transformations of planar vector fields of
Schr\"odinger 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.

View original: http://arxiv.org/abs/1111.0120