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Abstract
A generic solution of the Weyl relation HR = qRH is found, where H and R are discrete tridiagonal Schrödinger operators with real coefficients. This solution describes the two-parameter non-linear unitary automorphism of the quantum SL q (2) algebra. This leads to a new class of exactly solvable discrete Schrödinger equations having SL q (2) as dynamical symmetry.
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