New generalized coherent states

DOI10.1063/1.532869zbMath0953.81035OpenAlexW2044062338MaRDI QIDQ4701859

Allan I. Solomon, Karol A. Penson

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532869

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Coherent states (81R30) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (37)

Generalized coherent states associated with the \(C_ \lambda\)-extended oscillator. ⋮ Difference ladder operators for a harmonic Schrödinger oscillator using unitary linear lattices ⋮ Entanglement of photon-added nonlinear coherent states via a beam splitter ⋮ Truncated generalized coherent states ⋮ Coherent states and Hermite polynomials on quaternionic Hilbert spaces ⋮ ( p , q ) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation ⋮ Deformed Exterior Algebra, Quons and their Coherent States ⋮ On the Laplace transform of the Fréchet distribution ⋮ Dobiński relations and ordering of boson operators ⋮ New construction of coherent states for generalized harmonic oscillators ⋮ Optical Schrödinger cats with generalized coherent states ⋮ \(q\)-coherent states associated with the noncommutative complex plane \(\mathbb C_{q^2}\) for the Biedenharn-Macfarlane \(q\)-oscillator ⋮ Generalized coherent states of light interacting with a nonlinear medium, quantum superpositions and dissipative processes ⋮ Nonclassical properties of the Arik–Coon q−1-oscillator coherent states on the noncommutative complex plane ℂq ⋮ The truncated Stieltjes moment problem solved by using kernel density functions ⋮ Arik–Coon q-oscillator cat states on the noncommutative complex plane ℂq−1 and their nonclassical properties ⋮ Oscillatory difference equations and moment problems ⋮ Classical interpretation of a deformed quantum oscillator ⋮ Canonical and nonlinear vector coherent states of generalized models with spin-orbit interaction ⋮ On completeness of coherent states in noncommutative spaces with the generalised uncertainty principle ⋮ Using supermodels in quantum optics ⋮ Construction of the dual family of Gazeau–Klauder coherent states via temporally stable nonlinear coherent states ⋮ Some basic difference equations of Schrödinger boundary value problems ⋮ Temporally stable coherent states for infinite well and Pöschl–Teller potentials ⋮ Analytic aspects ofq-delayed exponentials: minimal growth, negative zeros and basic ghost states ⋮ Coherence, Squeezing and Entanglement: An Example of Peaceful Coexistence ⋮ Quantum groups \(GL_{p,q}(2)\)- and \(SU_{q_{1}/q_{2}}(2)\)-invariant bosonic gases: A Comparative study ⋮ Nonautonomous oscillators and coefficient evaluation for orthogonal function systems ⋮ On nonlinear coherent states properties for electron-phonon dynamics ⋮ Density operator representation in multi-matrix vector coherent states: Landau problem in a harmonic potential background ⋮ q -graded Heisenberg algebras and deformed supersymmetries ⋮ Quaternionic vector coherent states and the supersymmetric harmonic oscillator ⋮ Generalized coherent states for \(q\)-oscillator associated with discrete \(q\)-Hermite polynomials ⋮ Multi-dimensional q-deformed bosonic Newton oscillators and the related q-calculus, q-coherent states, and Hermite q-polynomials ⋮ Density operator formulation for a supersymmetric harmonic oscillator: vector coherent state construction and statistical properties ⋮ Nonclassicality of new class of states produced by superposition of two nonlinear squeezed states with respective phase \(\varphi\) ⋮ Special deformed exponential functions leading to more consistent Klauder's coherent states

Cites Work

• Quantization without quantization
• Optimal signal-to-quantum noise ratio for deformed photons
• Path-integral formalism for the supercoherent states
• 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
• Coherent states for isospectral oscillator Hamiltonians
• The quantum mechanical Schrodinger picture of a q-oscillator
• Hilbert spaces of analytic functions and generalized coherent states
• COHERENT STATES WITHOUT GROUPS: QUANTIZATION ON NONHOMOGENEOUS MANIFOLDS

This page was built for publication: New generalized coherent states