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

Book Contribution - Book Chapter Conference Contribution

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 3F2 and 2F1 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.
Book: Springer Proceedings in Mathematics & Statistics
Volume: 111
Pages: 291 - 299
ISBN:9784431552857
Accessibility:Closed