Dynamical algebra of the q-deformed three-dimensional oscillator

DOI10.1063/1.530138zbMath0787.17017OpenAlexW2103010148MaRDI QIDQ4201736

Joris Van der Jeugt

Publication date: 6 September 1993

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

Full work available at URL: https://doi.org/10.1063/1.530138

zbMATH Keywords

dynamical algebra\(q\)-deformed spherical tensor bosons\(q\)-deformed three-dimensional harmonic oscillator

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) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Cites Work

• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• The quantum group SU_q(2) and a q-analogue of the boson operators
• On the q oscillator and the quantum algebra su_q(1,1)
• Complementary group with respect to SO(n)
• Reduction of the unitary group to its orthogonal or symplectic subgroup: a unified approach based upon complementary groups
• WKB equivalent potentials for the q-deformed harmonic oscillator
• WKB equivalent potentials for q-deformed harmonic and anharmonic oscillators
• Linear Canonical Transformations and Their Unitary Representations
• Canonical Transformations and Matrix Elements
• SU_q(1,1) description of vibrational molecular spectra

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