Self-similar potentials and the \(q\)-oscillator algebra at roots of unity

DOI10.1007/BF00739567zbMath0778.17012arXivhep-th/9304107MaRDI QIDQ2366644

S. Skorik, Vyacheslav P. Spiridonov

Publication date: 11 January 1994

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9304107

zbMATH Keywords

\(q\)-deformed Heisenberg-Weyl algebraself-similar potentials

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (11)

Coherent states of the \(q\)-Weyl algebra ⋮ Exact and discretized stability of the pantograph equation ⋮ \(q\)-ultraspherical polynomials for \(q\) a root of unity ⋮ The pantograph equation in the complex plane ⋮ On some nonlinear functional-differential equations of neutral type with linear deviations of the argument ⋮ Self-similar potentials and \(q\)-coherent states ⋮ On the spectra of hyperelliptic potentials ⋮ On the spectrum of a \(q\)-oscillator with a linear interaction ⋮ Coherent state maps related to the bounded positive operators ⋮ Small divisors problem in dynamical systems and analytic solutions of the Shabat equation ⋮ Regular solutions of the Shabat equation

Cites Work

• Irreducible representations of the quantum analogue of SU(2)
• Algebra of functions on the quantum group SU(2)
• The infinite-dimensional dressing dynamical system
• Exactly solvable potentials and quantum algebras
• The Factorization Method

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