On a pair of difference equations for the $_4F_3$ type orthogonal polynomials and related exactly-solvable quantum systems

E. I. Jafarov; N. I. Stoilova; J. Van der Jeugt

doi:10.1007/978-4-431-55285-7_20

paper

On a pair of difference equations for the $_{4} F_{3}$ type orthogonal polynomials and related exactly-solvable quantum systems

arXiv:1411.6125 · doi:10.1007/978-4-431-55285-7_20

Abstract

We introduce a pair of novel difference equations, whose solutions are expressed in terms of Racah or Wilson polynomials depending on the nature of the finite-difference step. A number of special cases and limit relations are also examined, which allow to introduce similar difference equations for the orthogonal polynomials of the $_{3} F_{2}$ and $_{2} F_{1}$ types. It is shown that the introduced equations allow to construct new models of exactly-solvable quantum dynamical systems, such as spin chains with a nearest-neighbour interaction and fermionic quantum oscillator models.

8 pages, to be published in Springer Proceedings in Mathematics & Statistics

On a pair of difference equations for the 4​F3​ type orthogonal polynomials and related exactly-solvable quantum systems

Abstract

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On a pair of difference equations for the $_{4} F_{3}$ type orthogonal polynomials and related exactly-solvable quantum systems