Darboux transformation of coherent states for a Lobachevski plane

1997 ◽  
Vol 40 (9) ◽  
pp. 848-855
Author(s):  
B. F. Samsonov
Keyword(s):  
Darboux Transformation ◽  
Coherent States

HIGHER DERIVATIVE SUPERSYMMETRY, A MODIFIED CRUM–DARBOUX TRANSFORMATION AND COHERENT STATE

1999 ◽  
Vol 14 (01) ◽  
pp. 27-34 ◽  
Author(s):  
B. BAGCHI ◽  
A. GANGULY ◽  
D. BHAUMIK ◽  
A. MITRA
Keyword(s):  
Coherent State ◽  
Darboux Transformation ◽  
Coherent States ◽  
Second Derivative ◽  
Interesting Problem ◽  
Higher Derivative

Inspired by the possibility of factorizing the second derivative interwining operators using a modified form of the well-known Crum–Darboux transformation, we present a scheme for generating a new pair of isospectral potentials. We also consider the interesting problem of constructing coherent states for such factorizable operators.

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.

scholarly journals N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

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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