Speaker: Dr. Primitivo B. Acosta-Humánez

Invited Researcher, Instituto de Matemática

Universidad Autónoma de Santo Domingo

Title:  Liouvillian solutions for Schrödinger equations with Laurent polynomial potentials

Abstract:  This talk is devoted to a parametric study of Liouvillian solutions of Schrödinger equation with Laurent polynomial coefficients. This family of equations, for fixed orders at 0 and ∞ of the Laurent polynomial, is seen as an affine algebraic variety. We prove that the set of Picard-Vessiot integrable differential equations in the family is an enumerable union of algebraic subvarieties. We compute explicitly the algebraic equations of its components. Techniques include a combination of Kovacic Algorithm and Asymptotic Iteration Method (AIM). We give some applications to well known subfamilies as the doubly confluent and biconfluent Heun equations, and to the theory of algebraically solvable potentials of Shrödinger equations. Also, as an auxiliary tool, we improve a previously known criterion for second order linear differential equations to admit a polynomial solution. This is joint work with D. Blázquez-Sanz and H. Venegas-Gómez and is based on a paper recently accepted for publication in Journal of Symbolic Computation (see also https://arxiv.org/abs/2012.11795) 

https://zoom.us/j/97342598765?pwd=SzNxOU0za1I4RmdSRFh0STlKN0NtUT09