Generalized Coherent States Associated with the $C_{\lambda }$-Extended Oscillator

Abstract

Two new types of coherent states associated with the $C_{\lambda }$-extended oscillator, where $C_{\lambda }$ is the cyclic group of order $\lambda$, are introduced. They satisfy a unity resolution relation in the $C_{\lambda }$-extended oscillator Fock space (or in some subspace thereof) and give rise to Bargmann representations of the latter, wherein the generators of the $C_{\lambda }$-extended oscillator algebra are realized as differential-operator-valued matrices.

7 pages, LaTeX2e, no figure, communication at 2nd International Symposium Quantum Theory and Symmetries, Krakow, 18-21 July, 2001

References in corpus (6)

• f-Oscillators and Nonlinear Coherent States
• A family of complex potentials with real spectrum
• $C_{\lambda }$-extended harmonic oscillator and (para)supersymmetric quantum mechanics
• Non-linear coherent states associated with conditionally exactly solvable problems
• Spectrum generating algebra of the C_λ-extended oscillator and multiphoton coherent states
• Recursively minimally-deformed oscillators

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• Painlevé IV Coherent States
• Coherent states for ladder operators of general order related to exceptional orthogonal polynomials
• Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
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• Quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation
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• Deformed $C_{\lambda }$-Extended Heisenberg Algebra in Non-commutative Phase-Space