The \(q\)-deformed harmonic oscillator, coherent states, and the uncertainty relation

DOI10.1007/S11232-006-0072-YzbMath1177.81073arXiv0810.1967OpenAlexW2094312346MaRDI QIDQ1047969

A. A. Meldianov, V. V. Eremin

Publication date: 9 January 2010

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.1967

zbMATH Keywords

uncertainty relationcoherent states\(q\)-deformationharmonic oscillatorcreation operatorsannihilation operators

Mathematics Subject Classification ID

Coherent states (81R30) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (13)

Unnamed Item ⋮ Complexity study of \(q\)-deformed quantum harmonic oscillator ⋮ \(q\)-deformed quadrature operator and optical tomogram ⋮ An oscillator with position-dependent mass exposed to a thermal bosonic bath ⋮ RLC circuit realization of a q-deformed harmonic oscillator with time dependent mass ⋮ On the heat and wave equations with the Sturm-Liouville operator in quantum calculus ⋮ Investigation of the generalised Wigner-Dunkl harmonic oscillator and its coherent states ⋮ \(q\)-coherent states associated with the noncommutative complex plane \(\mathbb C_{q^2}\) for the Biedenharn-Macfarlane \(q\)-oscillator ⋮ Nonclassical properties of the Arik–Coon q−1-oscillator coherent states on the noncommutative complex plane ℂq ⋮ Arik–Coon q-oscillator cat states on the noncommutative complex plane ℂq−1 and their nonclassical properties ⋮ Quons, coherent states and intertwining operators ⋮ Deformed quons and bi-coherent states ⋮ The \(\mathrm q\)-deformed Dirac oscillator in \(2+1\) dimensions

Cites Work

• Even and odd \(q\)-deformed charge coherent states and their nonclassical properties
• Exact analytical expression for magnetoresistance using quantum groups
• A diagonal representation of the quantum density matrix using \(q\)-boson oscillator coherent states
• Observable properties of \(q\)-deformed physical systems
• A \(q\)-deformed uncertainty relation.
• \(q\)-deformed dynamics of \(q\)-deformed oscillators.
• 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)
• q-UNCERTAINTY RELATIONS
• Uncertainty relation in quantum mechanics with quantum group symmetry
• A Fock space representation for the quantum Lorentz gas

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