Regular two-point boundary value problems for the Schrödinger operator on a path

In this work we study the different type of regular boundary value problems on a path associated with the Schrödinger operator. In particular, we obtain the Green function for each problem and we emphasize the case of Sturm-Liouville boundary conditions. In any case, the Green function is given in t...

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Bibliographic Details
Published inElectronic notes in discrete mathematics Vol. 28; pp. 199 - 206
Main Authors Bendito, E., Carmona, A., Encinas, A.M., Gesto, J.M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2007
Subjects
Boundary value problems
Chebyshev polynomials
Discrete Schrödinger operator
Green function
Path
Path
Boundary value problems
Discrete Schrödinger operator
Green function
Chebyshev polynomials
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Summary:In this work we study the different type of regular boundary value problems on a path associated with the Schrödinger operator. In particular, we obtain the Green function for each problem and we emphasize the case of Sturm-Liouville boundary conditions. In any case, the Green function is given in terms of second kind Chebyshev polynomials since they verify a recurrence law similar to the one verified by the Schödinger operator on a path.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2007.01.027