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 Schr\"odinger equation with quasi-solvable polynomial potentials through the using of differential Galois theory and Gr\"obner basis. We illustrate these result...

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Bibliographic Details
Published in:arXiv.org 2019-05
Main Authors: Acosta-Humánez, Primitivo Belén, Venegas-Gómez, Henock
Format: Article
Language:English
Subjects:
Differential equations
Polynomials
Schrodinger equation
Online Access:Get full text
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Summary:The main aim of this paper is the presentation of a new methodology to obtain Liouvillian solutions of stationary one dimensional Schr\"odinger equation with quasi-solvable polynomial potentials through the using of differential Galois theory and Gr\"obner 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.
ISSN:2331-8422