arXiv:0906.1251 · Journal of Physics A Mathematical and Theoretical

Ladder operators and coherent states for continuous spectra

Joseph Ben Geloun, John R. Klauder

Published Aug 28, 2009• 13 citations

Abstract

The notion of ladder operators is introduced for systems with continuous spectra. We identify two different kinds of annihilation operators allowing the definition of coherent states as modified 'eigenvectors' of these operators. Axioms of Gazeau–Klauder are maintained throughout the construction.

DOI: 10.1088/1751-8113/42/37/375209

Related papers

Ladder operators and coherent states for nonlinear potentials

R. Román-Ancheyta, O de los Santos-Sánchez, J. Récamier

In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schrödinger equation. We show that both methods yield coherent states with identical algebraic structure.

arXiv:1503.01747Journal of Physics A Mathematical and TheoreticalOct 10, 201115 citations

Construction of coherent states for physical algebraic systems

Y. Hassouni, Evaldo M. F. Curado, M. A. Rego-Monteiro

We construct a general state which is an eigenvector of the annihilation operator of the generalized Heisenberg algebra. We show, for several systems characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder's minimal coherent states.

arXiv:math-ph/0408030Physical Review AFeb 11, 200543 citations

The Moyal bracket in the coherent states framework

Mohammed Daoud A, El Hassan El Kinani

The star product and Moyal bracket are introduced using the coherent states corresponding to quantum systems with non-linear spectra. Two kinds of coherent state are considered. The first kind is the set of Gazeau-Klauder coherent states and the second kind are constructed following the Perelomov-Klauder approach. The particular case of the harmonic oscillator is also discussed.

arXiv:math-ph/0309037Journal of Physics A Mathematical and GeneralMar 8, 200211 citations

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

G R Honarasa, M K Tavassoly, M Hatami +1 more

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. It is shown that, the main axioms of Gazeau-Klauder coherent states will be satisfied, properly. Nonclassical properties and quantum statistics of coherent states, as well as the introduced excited coherent states are discussed. In particular, through the study of quadrature squeezing and amplitude squared squeezing, it will be observed that both classes of the above states can be classified in the intelligent states category.

arXiv:1103.1643Journal of Physics A Mathematical and TheoreticalFeb 1, 20115 citations

Coherent states for a system of an electron moving in a plane

Isiaka Aremua, Laure Gouba

Abstract In this paper, we construct the coherent states for a system of an electron moving in a plane under uniform external magnetic and electric fields. These coherent states are built in the context of both discrete and continuous spectra and satisfy the Gazeau-Klauder coherent state properties Gazeau and Klauder (1999 J. Phys. A: Math. Gen. 32, 123–132).

arXiv:2106.07311Journal of Physics CommunicationsAug 1, 20213 citations

Some classes of finite-dimensional ladder operators

Fabio Bagarello, Antonino Faddetta, Francesco Oliveri

Abstract We introduce and study some special classes of ladder operators in finite-dimensional Hilbert spaces. In particular we consider a truncated version of quons, their pseudo-version, and a third family of operators acting on a closed chain. In this latter situation, we discuss the existence of what could be considered discrete coherent states, as suitable eigenvectors of the annihilation operator of the chain. We see that, under reasonable assumptions, a resolution of the identity can be recovered, involving these states, together with a biorthogonal family of vectors, which turn out to be eigenstates of the raising operator of the chain.

arXiv:2507.16629Journal of Physics A Mathematical and TheoreticalJul 21, 20250 citations