Bargmann Representations for Deformed Harmonic Oscillators

DOI10.1142/S0129055X98000343zbMath0960.81043arXivq-alg/9707020OpenAlexW3098024399MaRDI QIDQ4236092

Michèle Irac-Astaud, Guy Rideau

Publication date: 17 May 2001

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

Full work available at URL: https://arxiv.org/abs/q-alg/9707020

zbMATH Keywords

Bargmann representationsdeformed harmonic oscillatorsFock-representations

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Coherent states (81R30) Applications of functional analysis in quantum physics (46N50)

Related Items (2)

DEFORMED HARMONIC OSCILLATOR ALGEBRAS DEFINED BY THEIR BARGMANN REPRESENTATIONS ⋮ Nonclassicality of photon-added \(q\)-squeezed first excited states

Cites Work

• On coherent states for the simplest quantum groups
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• On the representations of quantum oscillator algebra
• Representations of generalized oscillator algebra
• Coherent states of the \(q\)-Weyl algebra
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• On a Hilbert space of analytic functions and an associated integral transform part I
• A q-analogue of Bargmann space and its scalar product
• The quantum group SU_q(2) and a q-analogue of the boson operators
• A completeness relation for the q-analogue coherent states by q-integration
• Complex analytic realizations for quantum algebras
• Coherent states for a quantum particle on a circle
• Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model
• q-exponential and q-gamma functions. I. q-exponential functionsa)

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