Self-similarity in Spectral Problems and q-special Functions

I. Loutsenko; V. Spiridonov

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Self-similarity in Spectral Problems and q-special Functions

I. Loutsenko·V. Spiridonov

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Abstract

Similarity symmetries of the factorization chains for one-dimensional differential and finite-difference Schrödinger equations are discussed. Properties of the potentials defined by self-similar reductions of these chains are reviewed. In particular, their algebraic structure, relations to $q$-special functions, infinite soliton systems, supersymmetry, coherent states, orthogonal polynomials, one-dimensional Ising chains and random matrices are outlined.

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I. Loutsenko, V. Spiridonov. 1999-09-21. Self-similarity in Spectral Problems and q-special Functions. https://arxiv.org/abs/solv-int/9909022

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