Semibounded symmetry operator transformation of nonrelativistic free-particle coherent states

1999 ◽  
Vol 42 (2) ◽  
pp. 142-148
Author(s):  
B. F. Samsonov ◽  
L. A. Shekoyan
Keyword(s):  
Coherent States ◽  
Free Particle ◽  
Symmetry Operator ◽  
Operator Transformation

Coherent States of Quantum Free Particle on the Spherical Space

2015 ◽  
Vol 55 (1) ◽  
pp. 124-136 ◽  
Author(s):  
Shahram Dehdashti ◽  
Rasoul Roknizadeh ◽  
Ali Mahdifar ◽  
Hongsheng Chen
Keyword(s):  
Coherent States ◽  
Free Particle ◽  
Spherical Space

scholarly journals Analyzing generalized coherent states for a free particle

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Mustapha Maamache ◽  
Abderrezak Khatir ◽  
Halim Lakehal ◽  
Jeong Ryeol Choi
Keyword(s):  
Coherent States ◽  
Free Particle ◽  
Generalized Coherent States

BARUT–GIRARDELLO COHERENT STATES CONSTRUCTED BY Ym m(θ,φ) AND Ym+1 m(θ,φ) FOR A FREE PARTICLE ON THE SPHERE

2004 ◽  
Vol 19 (35) ◽  
pp. 2619-2628 ◽  
Author(s):  
A. CHENAGHLOU ◽  
H. FAKHRI
Keyword(s):  
Lie Algebra ◽  
Coherent States ◽  
Free Particle ◽  
Irreducible Representations ◽  
Legendre Functions ◽  
Associated Legendre Functions ◽  
Shape Invariance ◽  
Infinite Dimensional ◽  
Direct Sum ◽  
Lowering Operator

Using the realization idea of simultaneous shape invariance with respect to two different parameters of the associated Legendre functions, the Hilbert space of spherical harmonics Yn m(θ,φ) corresponding to the motion of a free particle on a sphere is split into a direct sum of infinite-dimensional Hilbert subspaces. It is shown that these Hilbert subspaces constitute irreducible representations for the Lie algebra u (1,1). Then by applying the lowering operator of the Lie algebra u (1,1), Barut–Girardello coherent states are constructed for the Hilbert subspaces consisting of Ym m(θ,φ) and Ym+1 m(θ,φ).

Gazeau- Klouder Coherent states on a sphere

2019 ◽  
Vol 19 (2) ◽  
pp. 379-390
Author(s):  
Z Heibati ◽  
A Mahdifar ◽  
E Amooghorban ◽  
◽  
◽  
...  
Keyword(s):  
Coherent States

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

scholarly journals Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 250
Author(s):  
Frédéric Barbaresco ◽  
Jean-Pierre Gazeau
Keyword(s):  
Fourier Analysis ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Lie Groups ◽  
Coherent States ◽  
Geometric Theory ◽  
Plancherel Formula ◽  
Group Representations ◽  
Modern Development ◽  
Xxist Century

For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.

sl(2)-modules bysl(2)-coherent states

2016 ◽  
Vol 57 (9) ◽  
pp. 091704 ◽  
Author(s):  
H. Fakhri ◽  
M. Sayyah-Fard
Keyword(s):  
Coherent States
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