# Coherent States, Wavelets, and Their Generalizations

@inproceedings{Ali2013CoherentSW, title={Coherent States, Wavelets, and Their Generalizations}, author={Syed Twareque Ali and Jean-Pierre Antoine and J. P. Gazeau}, year={2013} }

This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their…

#### 418 Citations

Quantizations on the circle and coherent states

- Mathematics, Physics
- 2012

We present a possible construction of coherent states on the unit circle as configuration space. Our approach is based on Borel quantizations on S1 including the Aharonov–Bohm-type quantum…

Coherent State Quantization and Moment Problem

- Mathematics
- 2010

Berezin-Klauder-Toeplitz (“anti-Wick”) or “coherent state” quantization of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity…

A new class of f-deformed charge coherent states and their nonclassical properties

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- 2012

Two-mode charge (pair) coherent states have been introduced previously by using the ??| representation. In this paper, we reobtain these states by a rather different method. Then, using the nonlinear…

Coherent States for an Abstract Hamiltonian with a General Spectrum

- 2012

Following the method proposed by Gazeau and Klauder to construct temporally stable coherent states, CS for short, in recent years, several classes of CS were constructed for quantum Hamiltonians. The…

Conventional and Enhanced Canonical Quantizations, Application to Some Simple Manifolds

- Physics
- 2013

It is well known that the representations over an arbitrary configuration
space related to a physical system of the Heisenberg algebra allow to
distinguish the simply and non simply-connected…

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

- Physics, Mathematics
- 2011

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state…

On nonlinear coherent states properties for electron-phonon dynamics

- Physics, Mathematics
- 2013

This work addresses a construction of a dual pair of nonlinear coherent states (NCS) in the context of changes of bases in the underlying Hilbert space for a model pertaining to an electron-phonon…

Coherent states: a contemporary panorama

- Physics
- 2012

Coherent states (CS) of the harmonic oscillator (also called canonical CS) were introduced in 1926 by Schr?dinger in answer to a remark by Lorentz on the classical interpretation of the wave…

Complexified coherent states and quantum evolution with non-Hermitian Hamiltonians

- Physics, Mathematics
- 2011

The complex geometry underlying the Schr\"odinger dynamics of coherent states for non-Hermitian Hamiltonians is investigated. In particular two seemingly contradictory approaches are compared: (i) a…

Nonclassical properties of coherent states and excited coherent states for continuous spectra

- Mathematics, Physics
- 2011

Based on the definition of coherent states for continuous spectra and analogous to photon-added coherent states for discrete spectra, we introduce the excited coherent states for continuous spectra.…