Self-similarity in Spectral Problems and q-special Functions
solv-int
2007-05-23 v1 High Energy Physics - Theory
Exactly Solvable and Integrable Systems
Abstract
Similarity symmetries of the factorization chains for one-dimensional differential and finite-difference Schr\"odinger equations are discussed. Properties of the potentials defined by self-similar reductions of these chains are reviewed. In particular, their algebraic structure, relations to -special functions, infinite soliton systems, supersymmetry, coherent states, orthogonal polynomials, one-dimensional Ising chains and random matrices are outlined.
Keywords
Cite
@article{arxiv.solv-int/9909022,
title = {Self-similarity in Spectral Problems and q-special Functions},
author = {I. Loutsenko and V. Spiridonov},
journal= {arXiv preprint arXiv:solv-int/9909022},
year = {2007}
}