Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators

Abstract

We 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.

33 pages

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Cited by in corpus (8)

• Exactly Solvable Discrete Quantum Mechanical Systems and Multi-indexed Orthogonal Polynomials of the Continuous Hahn and Meixner-Pollaczek Types
• New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials V : Racah and $q$-Racah types
• Multiplication operator and exceptional Jacobi polynomials
• Dual Polynomials of the Multi-Indexed ($q$-)Racah Orthogonal Polynomials
• Spectral intertwining relations in exactly solvable quantum-mechanical systems
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types
• Asymptotics for Recurrence Coefficients of X1-Jacobi Polynomials and Christoffel Function