Quaternionic vector coherent states and the supersymmetric harmonic oscillator

2006 ◽  
Vol 149 (1) ◽  
pp. 1366-1381 ◽  
Author(s):  
K. Thirulogasanthar ◽  
A. Krzyżak ◽  
Q. D. Katatbeh
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Vector Coherent States

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

2001 ◽  
Vol 16 (02) ◽  
pp. 91-98 ◽  
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.

scholarly journals Lewis-Riesenfeld quantization and SU(1, 1) coherent states for 2D damped harmonic oscillator

2018 ◽  
Vol 59 (11) ◽  
pp. 112101 ◽  
Author(s):  
Latévi M. Lawson ◽  
Gabriel Y. H. Avossevou ◽  
Laure Gouba
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Damped Harmonic Oscillator

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Coherent States ◽  
Finite Interval ◽  
Hermite Polynomials ◽  
Oscillator Algebra ◽  
Text Representation ◽  
Ladder Operators ◽  
Recursion Relations ◽  
Wilson Operator

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

scholarly journals Groupoids and Coherent States

2019 ◽  
Vol 26 (04) ◽  
pp. 1950017 ◽  
Author(s):  
F. di Cosmo ◽  
A. Ibort ◽  
G. Marmo
Keyword(s):  
Hilbert Space ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum Mechanical ◽  
Natural Setting ◽  
Invariant Subset ◽  
Quantum Mechanical System ◽  
Generalized Coherent States ◽  
Invertible Elements ◽  
Groupoid Algebra

Schwinger’s algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids. Thus given a quantum mechanical system with associated Hilbert space determined by a representation of a groupoid, it is shown that any invariant subset of the group of invertible elements in the groupoid algebra determines a family of generalized coherent states provided that a completeness condition is satisfied. The standard coherent states for the harmonic oscillator as well as generalized coherent states for f-oscillators are exemplified in this picture.

Sign in / Sign up

Export Citation Format

Share Document