Connection factors in the Schrödinger equation with a polynomial potential

Given a second order differential equation with two singular points, namely the origin and infinity, the connection factors allow to split a power series solution into formal solutions with known asymptotic behavior. A procedure is suggested to obtain those factors, as quotients of Wronskians of the...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and applied mathematics 2007-10, Vol.207 (2), p.291-300
Main Authors: Gómez, Francisco J., Sesma, Javier
Format: Article
Language:English
Subjects:
Connection factors
Gamma functions
Heun equations
Schrödinger equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Given a second order differential equation with two singular points, namely the origin and infinity, the connection factors allow to split a power series solution into formal solutions with known asymptotic behavior. A procedure is suggested to obtain those factors, as quotients of Wronskians of the mentioned solutions, in the case of a Schrödinger equation with a polynomial potential. Application of the procedure to particular cases, whose connection factors are already known, allows us to obtain new relations for quotients and products of gamma functions.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2006.10.008