\(C_ \lambda\)-extended oscillator algebras and some of their deformations and applications to quantum mechanics.

DOI10.1023/A:1003627217508zbMath1035.81516arXivmath-ph/0003025OpenAlexW1756227501MaRDI QIDQ1590865

Christiane Quesne, Nicolas Vansteenkiste

Publication date: 1 January 2001

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0003025

zbMATH Keywords

unitary irreducible representations annihilation supersymmetric quantum mechanics Casimir operators number operators Calogero-Vasiliev algebra oscillator algebra of creation parasupersymmetric quantum mechanics pseudosupersymmetric and orthosupersymmetric quantum mechanics

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Supersymmetry and quantum mechanics (81Q60) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items (10)

Generalized coherent states associated with the \(C_ \lambda\)-extended oscillator. ⋮ Parasupersymmetry and \(\mathcal N\)-fold supersymmetry in quantum many-body systems. I: General formalism and second order ⋮ REDUCIBILITY AND BOSONIZATION OF PARASUPERSYMMETRIC AND ORTHOSUPERSYMMETRIC QUANTUM MECHANICS ⋮ Extended Weyl-Heisenberg algebra, phase operator, unitary depolarizers and generalized Bell states ⋮ \(C_ \lambda\)-extended harmonic oscillator and (para)supersymmetric quantum mechanics. ⋮ \(\kappa\)-deformed photon and Jaynes-Cummings model ⋮ \(C_\lambda\)-extended oscillator algebra and \(d\)-orthogonal polynomials ⋮ Generalized fermion algebra ⋮ PSEUDOSUPERSYMMETRIC QUANTUM MECHANICS: GENERAL CASE, ORTHOSUPERSYMMETRIES, REDUCIBILITY, AND BOSONIZATION ⋮ New algebraic structures in the \(C_{\lambda}\)-extended Hamiltonian system

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