Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1410.0305

Equivalent sets of coherent states of the 1D infinite square well and properties

Marc-Antoine Fiset, Véronique Hussin

Published Oct 1, 2014• 1 citation
arXivHTMLPDF

Abstract

We prove the equivalence (under some conditions) of two sets of coherent states built for the one-dimensional infinite square well: the so-called generalized and Gaussian Klauder coherent states. We then derive an approximate close expression approaching their probability density and wave function to explore their properties analytically. This process gives thereby explanation of the quasi-classical behavior of these states in terms of the main observables and the Heisenberg uncertainty product

DOI
10.48550/arxiv.1410.0305

Related papers

Supersymmetric infinite wells and coherent states

Marc-Antoine Fiset, Véronique Hussin

Gaussian Klauder coherent states are discussed in the context of the infinite well quantum model, otherwise known as the particle in a box. A supersymmetric partner system is also presented, as well as a construction of coherent states in this new system. We show that these states can be chosen, in both systems to have many properties usually expected for coherent states. In particular, they yield highly localised wave packets for a short period of time, which evolve in a quasi-classical manner and which saturate approximately Heisenberg uncertainty relation. These studies are elaborated in one- and two-dimensional contexts. Finally, some relations are established between the Gaussian states being mostly used here and the generalised coherent states, which are more standardly found in the literature.

arXiv:1502.05452•Journal of Physics Conference Series•Jun 26, 2015•10 citations

Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators

El Hassan El Kinani, Mohammed Daoud A

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system $[ 1] $. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states \\`{a} la Gazeau-Klauder and those \\`{a} la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways.

•Jan 1, 2001•8 citations

Coherent states of position-dependent mass trapped in an infinite square well

Naila Amir, Shahid Iqbal

We develop generalized coherent states based on the Gazeau–Klauder formalism for a particle with position-dependent mass trapped in an infinite square well. We study the quantum statistical properties of these states by means of the Mandel parameter and the second-order correlation function. Our analysis reveals that the constructed coherent states exhibit sub-Poissonian statistics. Moreover, theoretical investigations of wave packet revivals and fractional revivals for the pertaining system have been performed by means of the autocorrelation function and temporal evolution of probability density.

Journal of Mathematical Physics•Aug 1, 2020•12 citations

COHERENT AND GENERALIZED INTELLIGENT STATES FOR INFINITE SQUARE WELL POTENTIAL AND NONLINEAR OSCILLATORS

A. H. EL KINANI, Mohammed Daoud A

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system.1 We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau–Klauder and those à la Klauder–Perelomov, we derive the generalized intelligent states in analytical ways.

arXiv:quant-ph/0312122•International Journal of Modern Physics B•Oct 20, 2002•9 citations

Generalized coherent states and quantum-classical correspondence

Ronald F. Fox, Mee Hyang Choi

Gaussian Klauder coherent states are constructed for the harmonic oscillator, the planar rotor, and the particle in a box. The standard harmonic oscillator coherent states are given by expansions in the eigenstates of the Hamiltonian in terms of a complex parameter \ensuremath{\alpha}. When the complex modulus of \ensuremath{\alpha} is large, these states are identical in behavior with a particular choice of Gaussian Klauder coherent state. When the angular momentum of a planar rotor is large compared with Planck's constant, the angle distribution associated with a Gaussian Klauder coherent state for this case remains sharply localized for many rotations. Similarly, for the particle in a box, it is possible to choose parameters in the Gaussian Klauder coherent state so that a localized particle bounces back and forth at constant velocity between the walls of the box for many periods without significant delocalization. Buried in this behavior is the Fourier series for a triangle wave. These examples show how Gaussian Klauder coherent states are of utility in understanding quantum-classical correspondence.

Physical Review A•Feb 14, 2000•31 citations

Generalized coherent states and the quadratic Hamiltonian

Kanwarpreet S. Grewal

The idea of coherent states has proved very useful in the study of the quantum nature of electromagnetic radiation. Coherent states are also interesting because their evolution in time comes closest to classical dynamics. So they are the best approximation in quantum mechanics to classical behaviour. In recent years, attempts have been made to generalize the concept of coherent states to systems other than those made up of the simple harmonic oscillator (such as light). In one such attempt, Klauder introduces a set of physical criteria that generalized coherent states should have (Klauder J R 1996 J. Phys. A: Math. Gen. 29 L293). These criteria have been applied to the hydrogen atom and several other systems. In this paper, we apply Klauder's criteria to identify generalized coherent states for the quadratic Hamiltonian H = (f1a†a + f*2a2 + f2a†2). We check if two-photon coherent states of light satisfy these criteria. We find that they do not, which is expected: their non-classical properties are well known. We then use Klauder's criteria to find a set of states that are associated with the quadratic Hamiltonian. We find that these states too display non-classical behaviour even for large values of the quantum numbers. This non-classical behaviour is revealed in the form of sub-Poisson photon statistics. We will also briefly consider the one-photon Hamiltonian, apply Klauder's criteria to it and comment on its statistics.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 31, 2005•1 citation
We prove the equivalence (under some conditions) of two sets of coherent states built for the one-dimensional infinite square well: the so-called generalized and Gaussian Klauder coherent states. We then derive an approximate close expression approaching their probability density and wave function to explore their properties analytically. This process gives thereby explanation of the quasi-classical behavior of these states in terms of the main observables and the Heisenberg uncertainty product
Gaussian Klauder coherent states are discussed in the context of the infinite well quantum model, otherwise known as the particle in a box. A supersymmetric partner system is also presented, as well as a construction of coherent states in this new system. We show that these states can be chosen, in both systems to have many properties usually expected for coherent states. In particular, they yield highly localised wave packets for a short period of time, which evolve in a quasi-classical manner and which saturate approximately Heisenberg uncertainty relation. These studies are elaborated in one- and two-dimensional contexts. Finally, some relations are established between the Gaussian states being mostly used here and the generalised coherent states, which are more standardly found in the literature.
We develop generalized coherent states based on the Gazeau–Klauder formalism for a particle with position-dependent mass trapped in an infinite square well. We study the quantum statistical properties of these states by means of the Mandel parameter and the second-order correlation function. Our analysis reveals that the constructed coherent states exhibit sub-Poissonian statistics. Moreover, theoretical investigations of wave packet revivals and fractional revivals for the pertaining system have been performed by means of the autocorrelation function and temporal evolution of probability density.
Gaussian Klauder coherent states are constructed for the harmonic oscillator, the planar rotor, and the particle in a box. The standard harmonic oscillator coherent states are given by expansions in the eigenstates of the Hamiltonian in terms of a complex parameter \ensuremath{\alpha}. When the complex modulus of \ensuremath{\alpha} is large, these states are identical in behavior with a particular choice of Gaussian Klauder coherent state. When the angular momentum of a planar rotor is large compared with Planck's constant, the angle distribution associated with a Gaussian Klauder coherent state for this case remains sharply localized for many rotations. Similarly, for the particle in a box, it is possible to choose parameters in the Gaussian Klauder coherent state so that a localized particle bounces back and forth at constant velocity between the walls of the box for many periods without significant delocalization. Buried in this behavior is the Fourier series for a triangle wave. These examples show how Gaussian Klauder coherent states are of utility in understanding quantum-classical correspondence.
The idea of coherent states has proved very useful in the study of the quantum nature of electromagnetic radiation. Coherent states are also interesting because their evolution in time comes closest to classical dynamics. So they are the best approximation in quantum mechanics to classical behaviour. In recent years, attempts have been made to generalize the concept of coherent states to systems other than those made up of the simple harmonic oscillator (such as light). In one such attempt, Klauder introduces a set of physical criteria that generalized coherent states should have (Klauder J R 1996 J. Phys. A: Math. Gen. 29 L293). These criteria have been applied to the hydrogen atom and several other systems. In this paper, we apply Klauder's criteria to identify generalized coherent states for the quadratic Hamiltonian H = (f1a†a + f*2a2 + f2a†2). We check if two-photon coherent states of light satisfy these criteria. We find that they do not, which is expected: their non-classical properties are well known. We then use Klauder's criteria to find a set of states that are associated with the quadratic Hamiltonian. We find that these states too display non-classical behaviour even for large values of the quantum numbers. This non-classical behaviour is revealed in the form of sub-Poisson photon statistics. We will also briefly consider the one-photon Hamiltonian, apply Klauder's criteria to it and comment on its statistics.