2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94548Similarity 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.Exactly Solvable and Integrable SystemsHigh Energy Physics - Theorytext