2021-10-19T07:00:11Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000198212021-09-02T06:24:22Z1169:1170Recurrence relations of the multi-indexed orthogonal polynomials. IV. Closure relations and creation/annihilation operatorsOdake, SatoruWe consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types. Corresponding to the recurrence relations with constant coefficients for the M-indexed orthogonal polynomials, it is expected that the systems satisfy the generalized closure relations. In fact we can verify this statement for small M examples. The generalized closure relation gives the exact Heisenberg operator solution of a certain operator, from which the creation and annihilation operators of the system are obtained. Published by AIP Publishing.ArticleJOURNAL OF MATHEMATICAL PHYSICS. 57(11):113503 (2016)journal articleAMER INST PHYSICS2016-11application/pdfJOURNAL OF MATHEMATICAL PHYSICS11571135030022-2488AA00701758https://soar-ir.repo.nii.ac.jp/record/19821/files/1606.02836v1.pdfeng10.1063/1.4966985https://doi.org/10.1063/1.4966985© 2016 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. / The following article appeared in JOURNAL OF MATHEMATICAL PHYSICS. 57(11):113503 (2016) and may be found at (https://doi.org/10.1063/1.4966985).