scholarly journals Unified (p, q; α, β, ν; γ) −deformed oscillator algebra: Irreducible representations and induced deformed harmonic oscillator

2012 ◽  
Vol 53 (1) ◽  
pp. 013504 ◽  
Author(s):  
E. Baloitcha ◽  
M. N. Hounkonnou ◽  
E. B. Ngompe Nkouankam
Keyword(s):  
Harmonic Oscillator ◽  
Irreducible Representations ◽  
Oscillator Algebra ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

scholarly journals Irreducible Representations of Deformed Oscillator Algebra and q-Special Functions

1997 ◽  
Vol 12 (01) ◽  
pp. 153-158 ◽  
Author(s):  
E. V. Damaskinsky ◽  
P. P. Kulish
Keyword(s):  
Moment Problem ◽  
Special Functions ◽  
Hermite Polynomials ◽  
Irreducible Representations ◽  
Oscillator Algebra ◽  
Exponential Functions ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra ◽  
Classical Moment Problem

Different generators of a deformed oscillator algebra give rise to one-parameter families of q-exponential functions and q-Hermite polynomials. Connections of the Stieltjes and Hamburger classical moment problem with the corresponding resolution of unity are also pointed out.

scholarly journals The Two-dimensional Harmonic Oscillator on a Noncommutative Space with Minimal Uncertainties

10.14311/1799 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Sanjib Dey ◽  
Andreas Fring
Keyword(s):  
Harmonic Oscillator ◽  
Pt Symmetry ◽  
Exceptional Point ◽  
Noncommutative Space ◽  
Two Dimensional ◽  
Oscillator Algebra ◽  
Eigenvalue Spectrum ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat noncommutative space and employ it to study the eigenvalue spectrum for the harmonic oscillator on this space. The perturbative expression for the eigenenergy indicates that the model might possess an exceptional point at which the spectrum becomes complex and its PT-symmetry is spontaneously broken.

Solution of the Dirac equation with some superintegrable potentials by the quadratic algebra approach

2014 ◽  
Vol 29 (06) ◽  
pp. 1450028 ◽  
Author(s):  
S. Aghaei ◽  
A. Chenaghlou
Keyword(s):  
Dirac Equation ◽  
Quadratic Algebra ◽  
Two Dimensional ◽  
Oscillator Algebra ◽  
Quadratic Algebras ◽  
Energy Eigenvalues ◽  
Vector Potentials ◽  
Algebra Approach ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

The Dirac equation with scalar and vector potentials of equal magnitude is considered. For the two-dimensional harmonic oscillator superintegrable potential, the superintegrable potentials of E8 (case (3b)), S4 and S2, the Schrödinger-like equations are studied. The quadratic algebras of these quasi-Hamiltonians are derived. By using the realization of the quadratic algebras in a deformed oscillator algebra, the structure function and the energy eigenvalues are obtained.

scholarly journals THREE-PARAMETER (TWO-SIDED) DEFORMATION OF HEISENBERG ALGEBRA

2012 ◽  
Vol 27 (21) ◽  
pp. 1250114 ◽  
Author(s):  
A. M. GAVRILIK ◽  
I. I. KACHURIK
Keyword(s):  
Deformation Parameter ◽  
Particle Number ◽  
Heisenberg Algebra ◽  
Unusual Property ◽  
Oscillator Algebra ◽  
Number Operator ◽  
The Third ◽  
Defining Relation ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

A three-parametric two-sided deformation of Heisenberg algebra (HA), with p, q-deformed commutator in the L.H.S. of basic defining relation and certain deformation of its R.H.S., is introduced and studied. The third deformation parameter μ appears in an extra term in the R.H.S. as pre-factor of Hamiltonian. For this deformation of HA we find novel properties. Namely, we prove it is possible to realize this (p, q, μ)-deformed HA by means of some deformed oscillator algebra. Also, we find the unusual property that the deforming factor μ in the considered deformed HA inevitably depends explicitly on particle number operator N. Such a novel N-dependence is special for the two-sided deformation of HA treated jointly with its deformed oscillator realizations.

Representations of the deformed oscillator algebra for different choices of generators

2000 ◽  
Vol 100 (2) ◽  
pp. 2061-2076 ◽  
Author(s):  
V. V. Borzov ◽  
E. V. Damaskinskii ◽  
S. B. Yegorov
Keyword(s):  
Oscillator Algebra ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

On a family of photon-added deformed coherent states associated with two-parameter deformed boson oscillator algebra

2004 ◽  
Vol 82 (8) ◽  
pp. 623-646 ◽  
Author(s):  
M H Naderi ◽  
M Soltanolkotabi ◽  
R Roknizadeh
Keyword(s):  
Coherent States ◽  
Photon Number ◽  
Dimensional Subspace ◽  
Oscillator Algebra ◽  
Infinite Dimensional ◽  
Quadrature Squeezing ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra ◽  
Two Parameter ◽  
Infinite Dimensional Subspace

By introducing a generalization of the (p, q)-deformed boson oscillator algebra, we establish a two-parameter deformed oscillator algebra in an infinite-dimensional subspace of the Hilbert space of a harmonic oscillator without first finite Fock states. We construct the associated coherent states, which can be interpreted as photon-added deformed states. In addition to the mathematical characteristics, the quantum statistical properties of these states are discussed in detail analytically and numerically in the context of conventional as well as deformed quantum optics. Particularly, we find that for conventional (nondeformed) photons the states may be quadrature squeezed in both cases Q = pq < 1, Q = pq > 1 and their photon number statistics exhibits a transition from sub-Poissonian to super-Poissonian for Q < 1 whereas for Q > 1 they are always sub-Poissonian. On the other hand, for deformed photons, the states are sub-Poissonian for Q > 1 and no quadrature squeezing occurs while for Q < 1 they show super-Poissonian behavior and there is a simultaneous squeezing in both field quadratures.PACS Nos.: 42.50.Ar, 03.65.–w

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