On the q oscillator and the quantum algebra su<sub>q</sub>(1,1)

Kulish, P. P.; Damaskinsky, E. V.

doi:10.1088/0305-4470/23/9/003

Cited by 352 publications

(195 citation statements)

References 8 publications

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“…3 The q-deformed so (4) We choose to deform the so(4) = su(2) ⊕ su(2) dynamical symmetry of the hydrogen atom by a parameter q by means of the well-established theory of the quantum group su q (2) [20,21,22,23], where the commutation relations are written as…”

Section: Undeformed Casementioning

confidence: 99%

Physics of the so q (4) hydrogen atom

Castro

Kullock

2015

Theor Math Phys

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In this work we investigate the q-deformation of the so(4) dynamical symmetry of the hydrogen atom using the theory of the quantum group su q (2). We derive the energy spectrum in a physically consistent manner and find a degeneracy breaking as well as a smaller Hilbert space. We point out that using the deformed Casimir as was done before leads to inconsistencies in the physical interpretation of the theory.

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Section: Undeformed Casementioning

confidence: 99%

Physics of the so q (4) hydrogen atom

Castro

Kullock

2015

Theor Math Phys

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“…Following [10,11,12,13,14], up to minor differences in the conventions, we consider a one dimensional q-deformed oscillator algebra for the creation and annihilation operators A † and A in the form AA † − q 2 A † A = 1, for q ≤ 1.…”

Section: Generalized Time-dependent Q-deformed Coherent Statesmentioning

confidence: 99%

Time-dependentq-deformed coherent states for generalized uncertainty relations

et al. 2013

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. We investigate properties of generalized time-dependent q-deformed coherent states for a noncommutative harmonic oscillator. The states are shown to satisfy a generalized version of Heisenberg's uncertainty relations. For the initial value in time the states are demonstrated to be squeezed, i.e. the inequalities are saturated, whereas when time evolves the uncertainty product oscillates away from this value albeit still respecting the relations. For the canonical variables on a noncommutative space we verify explicitly that Ehrenfest's theorem hold at all times. We conjecture that the model exhibits revival times to infinite order. Explicit sample computations for the fractional revival times and superrevival times are presented. Permanent repository link

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“…A different version of the deformed harmonic oscillator can be obtained by defining 43,46,47 This oscillator has been first introduced by Arik and Coon 38 and later considered also by Kuryshkin 39 . One then easily finds that 4) where Q = q 2 and Q-numbers are defined in (6.1).…”

Section: The Q-deformed Harmonic Oscillatormentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

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Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools (q-numbers, q-analysis, q-oscillators, q-algebras), the su q (2) rotator model and its extensions, the construction of deformed exactly soluble models (u(3)⊃so (3) model, Interacting Boson Model, Moszkowski model), the 3-dimensional q-deformed harmonic oscillator and its relation to the nuclear shell model, the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to the structure of molecules and of atomic clusters, as well as an outlook are also given.

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On the q oscillator and the quantum algebra su_q(1,1)

Cited by 352 publications

References 8 publications

Physics of the so q (4) hydrogen atom

Physics of the so q (4) hydrogen atom

Time-dependentq-deformed coherent states for generalized uncertainty relations

Quantum groups and their applications in nuclear physics

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On the q oscillator and the quantum algebra suq(1,1)

Cited by 352 publications

References 8 publications

Physics of the so q (4) hydrogen atom

Physics of the so q (4) hydrogen atom

Time-dependentq-deformed coherent states for generalized uncertainty relations

Quantum groups and their applications in nuclear physics

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On the q oscillator and the quantum algebra su_q(1,1)