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

AIP conference proceedings

Coherent States for One-Dimensional Systems

David J. Fernández C.

Published Jan 1, 2006• 2 citations
Publisher

Abstract

Coherent states are constructed for one‐dimensional Hamiltonians whose spectra are composed of an infinite number of discrete energy levels depending analytically on the index labeling them. The harmonic oscillator and infinite well potentials are used to illustrate the technique.
DOI
10.1063/1.2160971

Related papers

Coherent states for Hamiltonians generated by supersymmetry

David J Fernández, Véronique Hussin, Oscar Rosas-Ortiz

Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated to the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Poeschl-Teller potentials.

arXiv:0705.0316•Journal of Physics A Mathematical and Theoretical•May 30, 2007•75 citations

Coherent states for the damped harmonic oscillator

Kyu Hwang Yeon, Chung‐In Um, Thomas F. George

Using the Caldirola-Kanai Hamiltonian for the damped harmonic oscillator, exact coherent states are constructed. These new coherent states satisfy the properties which coherent states should generally have.

Physical Review A•Dec 1, 1987•81 citations

The pairing Hamiltonian for one pair of nucleons bound in a potential well

M. B. Barbaro, L. Fortunato, Alfredo Molinari +1 more

The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing, in the Hamiltonian formalism, even Grassmann variables. The eigenvectors are analytically expressed solely in terms of these with coefficients fixed by the eigenvalues and the single particle energies. For these a specific model is needed: in the case of the harmonic oscillator well, for any strength of the pairing interaction, an accurate expression is derived for both the collective eigenvalue and for those trapped in between the single particle levels. Notably the latter are labelled through an index upon which they depend parabolically.

arXiv:nucl-th/0012004•Dec 1, 2000•0 citations

Coherent states for a generalization of the harmonic oscillator

David J. Fernández C., Véronique Hussin, Luis Miguel Nieto

Coherent states for a family of isospectral oscillator Hamiltonians are derived from a suitable choice of annihilation and creation operators. The Fock-Bargmann representation is also obtained.

•Jan 1, 1995•0 citations

Quantum state engineering in finite-dimensional Hilbert space

Adam Miranowicz, W. Leoński, Sigurd Dyrting +1 more

We give a recipe for how to generate various harmonic oscillator states formally defined in finite-dimensional Hilbert space.

Acta Physica Slovaca Reviews and Tutorials•Jun 1, 1996•17 citations

Linearized coherent states for Hamiltonian systems with two equidistant ladder spectra

David Bermúdez, Alonso Contreras-Astorga, David J. Fernández C.

A simple way to construct exactly solvable Hamiltonians whose spectra contain two equidistant ladders, one finite and another infinite, appears when applying supersymmetric quantum mechanics to the harmonic oscillator. Some of those supersymmetric partners have third order differential ladder operators, although the order of the transformation is higher than one. In this work the linearized coherent states for these specific Hamiltonians are studied. To each SUSY partner Hamiltonian corresponds two families of linearized coherent states: one inside the subspace associated with the isospectral part of the spectrum and another one in the finite subspace generated by the states inserted through the SUSY technique.

Journal of Physics Conference Series•May 12, 2014•2 citations
The problem of one pair of identical nucleons sitting in N{\cal N}N single particle levels of a potential well and interacting through the pairing force is treated introducing, in the Hamiltonian formalism, even Grassmann variables. The eigenvectors are analytically expressed solely in terms of these with coefficients fixed by the eigenvalues and the single particle energies. For these a specific model is needed: in the case of the harmonic oscillator well, for any strength of the pairing interaction, an accurate expression is derived for both the collective eigenvalue and for those trapped in between the single particle levels. Notably the latter are labelled through an index upon which they depend parabolically.
A simple way to construct exactly solvable Hamiltonians whose spectra contain two equidistant ladders, one finite and another infinite, appears when applying supersymmetric quantum mechanics to the harmonic oscillator. Some of those supersymmetric partners have third order differential ladder operators, although the order of the transformation is higher than one. In this work the linearized coherent states for these specific Hamiltonians are studied. To each SUSY partner Hamiltonian corresponds two families of linearized coherent states: one inside the subspace associated with the isospectral part of the spectrum and another one in the finite subspace generated by the states inserted through the SUSY technique.