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We introduce a pair of novel difference equations, whose solutions areexpressed in terms of Racah or Wilson polynomials depending on the nature ofthe finite-difference step. A number of special cases and limit relations arealso examined, which allow to introduce similar difference equations for theorthogonal polynomials of the $ _3 F_2$ and $ _2 F_1$ types. It is shown thatthe introduced equations allow to construct new models of exactly-solvablequantum dynamical systems, such as spin chains with a nearest-neighbourinteraction and fermionic quantum oscillator models.

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