Connection factors in the Schrödinger equation with a polynomial potential

Authors:
Francisco J. Gómez;Javier Sesma
Affiliations:
Departamento de Física Teórica, Facultad de Ciencias, University of Zaragoza, 50009 Zaragoza, Spain;Departamento de Física Teórica, Facultad de Ciencias, University of Zaragoza, 50009 Zaragoza, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

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 Schrodinger 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.