ON q-DEFORMED PARA OSCILLATORS AND PARA-q OSCILLATORS

Three generalized commutation relations for a single mode of the harmonic oscillator which contains para-bose and q oscillator commutation relations are constructed. These are shown to be inequivalent. The coherent states of the annihilation operator for these three cases are also constructed.

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Photon added coherent states of the parity deformed oscillator

Modern Physics Letters A ◽

10.1142/s0217732319501049 ◽

2019 ◽

Vol 34 (14) ◽

pp. 1950104 ◽

Cited By ~ 4

Author(s):

A. Dehghani ◽

B. Mojaveri ◽

S. Amiri Faseghandis

Keyword(s):

Coherent States ◽

Uncertainty Relation ◽

Annihilation Operator ◽

Single Mode ◽

Heisenberg Algebra ◽

Uncertainty Relations ◽

Deformed Oscillator ◽

Cat States ◽

Poissonian Statistics ◽

Creation Operators

Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.[Formula: see text] The RDCSs minimize a corresponding uncertainty relation, and resolve an identity condition through a positive definite measure which is explicitly derived. We introduce a class of single-mode excited coherent states (PARDCS) of the PHO through “m” times application of deformed creation operators to RDCS. For the states thus constructed, we analyze their statistical properties such as squeezing and sub-Poissonian statistics as well as their uncertainty relations.

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DEFORMED HARMONIC OSCILLATOR AND NONLINEAR COHERENT STATES: NONCOMMUTATIVE QUANTUM SPACE APPROACH

International Journal of Modern Physics A ◽

10.1142/s0217751x09043043 ◽

2009 ◽

Vol 24 (10) ◽

pp. 1963-1986 ◽

Cited By ~ 4

Author(s):

MOHAMMAD HOSSEIN NADERI ◽

MAHMOOD SOLTANOLKOTABI ◽

RASOUL ROKNIZADEH

Keyword(s):

Harmonic Oscillator ◽

Coherent States ◽

Differential Calculus ◽

Quantum Plane ◽

Quantum Harmonic Oscillator ◽

Commutation Relations ◽

Noncommutative Differential Calculus ◽

Two Parameter ◽

Noncommutative Quantum ◽

Space Approach

In this paper, by using the Wess–Zumino formalism of noncommutative differential calculus, we show that the concept of nonlinear coherent states originates from noncommutative geometry. For this purpose, we first formulate the differential calculus on a GL p, q(2) quantum plane. By using the commutation relations between coordinates and their interior derivatives, we then construct the two-parameter (p, q)-deformed quantum phase space together with the associated deformed Heisenberg commutation relations. Finally, by applying the obtained results for the quantum harmonic oscillator we construct the associated coherent states, which can be identified as nonlinear coherent states. Furthermore, we show that some of the well-known deformed (nonlinear) coherent states, such as two-parameter (p, q)-deformed coherent states, Maths-type q-deformed coherent states, Phys-type q-deformed coherent states and Quesne deformed coherent states, can be easily obtained from our treatment.

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ON PARASUPERSYMMETRIC COHERENT STATES

Modern Physics Letters A ◽

10.1142/s0217732389001404 ◽

1989 ◽

Vol 04 (13) ◽

pp. 1209-1215 ◽

Cited By ~ 18

Author(s):

J. BECKERS ◽

N. DEBERGH

Keyword(s):

Harmonic Oscillator ◽

Coherent States ◽

Annihilation Operator

We determine a parasupersymmetric annihilation operator for the (l-dimensional) harmonic oscillator and construct its eigenstates leading to a basis of parasupersymmetric coherent states with expected degeneracies according to the work of Rubakov and Spiridonov.

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q-PHASE OPERATOR IN A FINITE-DIMENSIONAL HILBERT SPACE

Modern Physics Letters A ◽

10.1142/s0217732395000387 ◽

1995 ◽

Vol 10 (04) ◽

pp. 347-357 ◽

Cited By ~ 6

Author(s):

YAPING YANG ◽

ZURONG YU

Keyword(s):

Hilbert Space ◽

Electromagnetic Field ◽

Harmonic Oscillator ◽

Coherent States ◽

Single Mode ◽

Phase Operator ◽

Finite Dimensional ◽

Dimensional Hilbert Space ◽

Finite Dimensional Hilbert Space ◽

Phase Operators

In this letter, the unitary and Hermitian phase operators for the single-mode electromagnetic field are given in the q-deformed case. A new kind of q-coherent states of a q-harmonic oscillator in a finite-dimensional Hilbert space are introduced. Some properties of these operators and q-coherent states are discussed.

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NON-HERMITIAN OSCILLATOR-LIKE HAMILTONIANS AND λ-COHERENT STATES REVISITED

Modern Physics Letters A ◽

10.1142/s021773230100295x ◽

2001 ◽

Vol 16 (02) ◽

pp. 91-98 ◽

Cited By ~ 9

Author(s):

JULES BECKERS ◽

NATHALIE DEBERGH ◽

JOSÉ F. CARIÑENA ◽

GIUSEPPE MARMO

Keyword(s):

Harmonic Oscillator ◽

Hilbert Spaces ◽

Coherent States ◽

Scalar Product ◽

Points Of View ◽

Usual Scalar ◽

Usual Scalar Product

Previous λ-deformed non-Hermitian Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to take into account their property of self-adjointness. The corresponding deformed λ-states lead to new families of coherent states according to the DOCS, AOCS and MUCS points of view.

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(ANTI)COMMUTATIVITY OF THE HARMONIC CREATION AND ANNIHILATION OPERATORS

International Journal of Modern Physics B ◽

10.1142/s0217979206034327 ◽

2006 ◽

Vol 20 (11n13) ◽

pp. 1808-1818

Author(s):

S. KUWATA ◽

A. MARUMOTO

Keyword(s):

Irreducible Representation ◽

Harmonic Oscillator ◽

Linear Algebra ◽

Commutation Relation ◽

Complex Number ◽

Single Mode ◽

Equation Of Motion ◽

Sufficient Condition ◽

Special Linear ◽

Creation And Annihilation Operators

It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.

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