Invariant analytic orthonormalization procedure with an application to coherent states
@article{Bagarello2007InvariantAO,
title={Invariant analytic orthonormalization procedure with an application to coherent states},
author={Fabio Bagarello and Salvatore Triolo},
journal={Journal of Mathematical Physics},
year={2007},
volume={48},
pages={043505-043505}
}We discuss a general strategy which produces an orthonormal set of vectors, stable under the action of a given set of unitary operators Aj, j=1,2,…,n, starting from a fixed normalized vector in H and from a set of unitary operators. We discuss several examples of this procedure and, in particular, we show how a set of coherentlike vectors can be produced and in which condition over the lattice spacing this can be done.
6 Citations
An invariant analytic orthonormalization procedure with applications
- Mathematics
- 2007
We apply the orthonormalization procedure previously introduced by Bagarello and Triolo [J. Math. Phys. 48, 043505 (2007)] and adopted in connection with coherent states to Gabor frames and other…
Gabor-like systems in L2(Rd) and extensions to wavelets
- Mathematics
- 2008
In this paper we show how to construct a certain class of orthonormal bases in L 2 (R d ) starting from one or more Gabor orthonormal bases in L 2 (R). Each such basis can be obtained acting on a…
Gabor-like systems in and extensions to wavelets
- Mathematics
- 2008
In this paper we show how to construct a certain class of orthonormal bases in starting from one or more Gabor orthonormal bases in . Each such basis can be obtained acting on a single function with…
Extensions of the Noncommutative Integration
- Mathematics
- 2016
In this paper we will continue the analysis undertaken in Bagarello et al. (Rend Circ Mat Palermo (2) 55:21–28, 2006), Bongiorno et al. (Rocky Mt J Math 40(6):1745–1777, 2010), Triolo (Rend Circ Mat…
A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009
- Mathematics
- 2015
(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…
References
SHOWING 1-10 OF 12 REFERENCES
PAINLESS NONORTHOGONAL EXPANSIONS
- Mathematics
- 1986
In a Hilbert space H, discrete families of vectors {hj} with the property that f=∑j〈hj‖ f〉hj for every f in H are considered. This expansion formula is obviously true if the family is an orthonormal…
Bargmann transform, Zak transform, and coherent states
- Mathematics
- 1982
It is well known that completeness properties of sets of coherent states associated with lattices in
the phase plane can be proved by using the Bargmann representation or by using the kq …
Localization properties and wavelet-like orthonormal basesfor the lowest Landau level
- Physics
- 2001
As an illustration of the phase space localization problem of quantum mechanical systems, we study a two-dimensional electron gas in a magnetic field, such as encountered in the Fractional Quantum…
Dynamics of Electrons in Solids in External Fields
- Physics
- 1968
A quantum-mechanical representation is defined by means of finite translations in direct and reciprocal space. The eigenfunctions of the finite translations are found and their connection with Bloch…
COHERENT STATES: APPLICATIONS IN PHYSICS AND MATHEMATICAL PHYSICS
- Physics, Education
- 1985
This volume is a review on coherent states and some of their applications. The usefulness of the concept of coherent states is illustrated by considering specific examples from the fields of physics…
Coherent States
- PhysicsCompendium of Quantum Physics
- 2009
Coherent states (of the harmonic oscillator) were introduced by Erwin Schrödinger (1887-1961) at the very beginning of quantum mechanics in response to a complaint by Lorentz that Schrödinger’s wave…
Quantum corrections to the Wigner crystal: A Hartree-Fock expansion.
- PhysicsPhysical review. B, Condensed matter
- 1993
The quantum corrections to the two-dimensional Wigner crystal, for filling ν≤1/3, are discussed by using a Hartree-Fock expansion based on wave functions which are (i) related to one another by…
Ten Lectures on Wavelets
- Geology
- 1992
This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.