English

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 qq-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}
}
R2 v1 2026-07-22T20:09:15.897Z