Orthogonal Polynomials from Hermitian Matrices

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dc.creatorOdake, Satoru
dc.creatorSasaki, Ryu
dc.date2007-12-26
dc.date2008-02-27
dc.date.accessioned2026-07-07T11:54:51Z
dc.date.available2026-07-07T11:54:51Z
dc.descriptionA unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schrödinger equations. The hermitian matrices (factorisable Hamiltonians) are real symmetric tri-diagonal (Jacobi) matrices corresponding to second order difference equations. By solving the eigenvalue problem in two different ways, the duality relation of the eigenpolynomials and their dual polynomials is explicitly established. Through the techniques of exact Heisenberg operator solution and shape invariance, various quantities, the two types of eigenvalues (the eigenvalues and the sinusoidal coordinates), the coefficients of the three term recurrence, the normalisation measures and the normalisation constants etc. are determined explicitly.
dc.description53 pages, no figures. Several sentences and a reference are added. To be published in J. Math. Phys
dc.identifierhttps://arxiv.org/abs/0712.4106
dc.identifierhttp://arxiv.org/abs/0712.4106
dc.identifierJ.Math.Phys.49:053503,2008
dc.identifierdoi:10.1063/1.2898695
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/205052
dc.subjectClassical Analysis and ODEs
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.titleOrthogonal Polynomials from Hermitian Matrices
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