arXiv subjects

Primitivo Belén Acosta-Humánez

Publications and source records attributed to Primitivo Belén Acosta-Humánez.

2 recordsLinked to original sources

arXiv2019

Liouvillian Solutions of Schrödinger Equation with Polynomial Potentials using Gröbner Basis

The main aim of this paper is the presentation of a new methodology to obtain Liouvillian solutions of stationary one dimensional Schrödinger equation with quasi-solvable polynomial potentials through the using of differential Galois theory and Gröbner basis. We illustrate these results by the computing of polynomial potentials of degree 4, 6, 8, 10, 12, 14. Moreover, we show an implementation in \textbf{Mathematica} for the decatic potential.

math-ph↗

arXiv2018

Some tastings in Morales-Ramis Theory

In this paper we present a short material concerning to some results in Morales-Ramis theory, which relates two different notions of integrability: Integrability of Hamiltonian Systems through Liouville Arnold Theorem and Integrability of Linear Differential Equations through Differential Galois Theory. As contribution, we obtain the abelian differential Galois group of the variational equation related to a bi-parametric Hamiltonian system,

math.CA↗