Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0612166

Coherent States for generalized oscillator with finite-dimensional Hilbert space

Вадим Васильевич Борзов, Eugene V. Damaskinsky

Published Dec 19, 2006• 1 citation
arXivHTMLPDF

Abstract

The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As example we consider the generalized oscillator connected with Krawtchouk polynomials.
DOI
10.48550/arxiv.quant-ph/0612166

Related papers

Coherent states of Krawtchouk oscillator and beyond

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

In the frame of our approach we constructed the generalized oscillator connected with Krawtchouk polynomials (named Krawtchouk oscillator) and coherent states for this oscillator too. Ours results are compared with analogues ones obtained for another variant of Krawtchouk oscillator in the paper [N.M.Atakishiev and S.K.Suslov, Difference analogs of the harmonic oscillator, Teor. Mat. Fiz., 85, 64-73 (1990)] from other point of view. Our definition of coherent states is close to one given in [B.Roy and P.Roy, Phase properties of a new nonlinear coherent state, quant-ph/0002043] This investigation is partially supported by RFBR grant No 06-01-00451

arXiv:math-ph/0612071•Days on Diffraction•Jan 1, 2006•0 citations

Coherent states, even and odd coherent states in a finite-dimensional Hilbert space and their properties

Barnana Roy, Papai Roy

We have considered a harmonic oscillator in a finite-dimensional Hilbert space spanned by orthogonal polynomials of a discrete variable and constructed coherent states as well as even and odd coherent states of this oscillator. Various properties such as squeezing and antibunching of these states have also been examined.

Journal of Physics A Mathematical and General•Jan 30, 1998•18 citations

Generalized squeezed–coherent states of the finite one-dimensional oscillator and matrix multi-orthogonality

Vincent X. Genest, Luc Vinet, Alexei S. Zhedanov

A set of generalized squeezed–coherent states for the finite oscillator is obtained. These states are given as linear combinations of the mode eigenstates with amplitudes determined by matrix elements of exponentials in the generators. These matrix elements are given in the ( N + 1)-dimensional basis of the finite oscillator eigenstates and are seen to involve 3 × 3 matrix multi-orthogonal polynomials Q n ( k ) in a discrete variable k which have the Krawtchouk and vector-orthogonal polynomials as their building blocks. The algebraic setting allows for the characterization of these polynomials and the computation of mean values in the squeezed–coherent states. In the limit where N goes to infinity and the discrete oscillator approaches the standard harmonic oscillator, the polynomials tend to 2 × 2 matrix orthogonal polynomials and the squeezed–coherent states tend to those of the standard oscillator.

arXiv:1202.3410•Journal of Physics A Mathematical and Theoretical•May 4, 2012•3 citations

Generalized coherent states for oscillator connected with meixner polynomials

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

We extend our approach to constmction of coherent states for oscillator-like systems connected with given system of orthogonal polynomials to the case of the classical orthogonal polynomials of a discrete variable. In this paper we consider oscillntmor-liksey stem associated with the Meixnct polynomials and compare associated Hamiltonian with the Hamiltonian of the relativistic linear oscillator obtained by the other point of view. We also construct generalized coherent states both Rarut-Girardello and Perelomov types €or this system.

Days on Diffraction•Jan 1, 2004•3 citations

Generalized coherent states for classical orthogonal polynomials

Вадим Васильевич Борзов

For oscillator-like systems, connected with the Laguerre, Legendre and Chebyshev polynomials, coherent states of Glauber-Barut-Girardello type are defined. The suggested construction can be applied to each system of orthogonal polynomials including classical ones as well as deformed ones.

arXiv:math/0209181•Jan 1, 2002•9 citations

Generalized Coherent States for q-oscillator connected with discrete q-Hermite polynomials

Вадим Васильевич Борзов, Eugene V. Damaskinsky

We are continuing here the study of generalized coherent states of Barut-Girardello type for the oscillator-like systems connected with the given set of orthogonal polynomials. In this work we construct the family of coherent states associated with discrete $q$-Hermite polynomials of the II-type and prove the over-completeness of this family of states by constructing the measure for unity decomposition for this family of coherent states.

arXiv:quant-ph/0407252•Jul 29, 2004•2 citations
In the frame of our approach we constructed the generalized oscillator connected with Krawtchouk polynomials (named Krawtchouk oscillator) and coherent states for this oscillator too. Ours results are compared with analogues ones obtained for another variant of Krawtchouk oscillator in the paper [N.M.Atakishiev and S.K.Suslov, Difference analogs of the harmonic oscillator, Teor. Mat. Fiz., 85, 64-73 (1990)] from other point of view. Our definition of coherent states is close to one given in [B.Roy and P.Roy, Phase properties of a new nonlinear coherent state, quant-ph/0002043] This investigation is partially supported by RFBR grant No 06-01-00451
A set of generalized squeezed–coherent states for the finite oscillator is obtained. These states are given as linear combinations of the mode eigenstates with amplitudes determined by matrix elements of exponentials in the generators. These matrix elements are given in the ( N + 1)-dimensional basis of the finite oscillator eigenstates and are seen to involve 3 × 3 matrix multi-orthogonal polynomials Q n ( k ) in a discrete variable k which have the Krawtchouk and vector-orthogonal polynomials as their building blocks. The algebraic setting allows for the characterization of these polynomials and the computation of mean values in the squeezed–coherent states. In the limit where N goes to infinity and the discrete oscillator approaches the standard harmonic oscillator, the polynomials tend to 2 × 2 matrix orthogonal polynomials and the squeezed–coherent states tend to those of the standard oscillator.
We extend our approach to constmction of coherent states for oscillator-like systems connected with given system of orthogonal polynomials to the case of the classical orthogonal polynomials of a discrete variable. In this paper we consider oscillntmor-liksey stem associated with the Meixnct polynomials and compare associated Hamiltonian with the Hamiltonian of the relativistic linear oscillator obtained by the other point of view. We also construct generalized coherent states both Rarut-Girardello and Perelomov types €or this system.
We are continuing here the study of generalized coherent states of Barut-Girardello type for the oscillator-like systems connected with the given set of orthogonal polynomials. In this work we construct the family of coherent states associated with discrete qqq-Hermite polynomials of the II-type and prove the over-completeness of this family of states by constructing the measure for unity decomposition for this family of coherent states.