Tuesday, April 23, 2013

1304.5698 (Primitivo B. Acosta-Humánez et al.)

Liouvillian Propagators, Riccati Equation and Differential Galois Theory    [PDF]

Primitivo B. Acosta-Humánez, Erwin Suazo
In this note a Galoisian approach to build propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schr\"odinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As an application we find the propagator for a generalized harmonic oscillator that has applications describing the process of degenerate parametric amplification in quantum optics and the description the light propagation in a nonlinear anisotropic waveguide.
View original: http://arxiv.org/abs/1304.5698

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