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

Coherent states for a generalization of the harmonic oscillator

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

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

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.

Related papers

Coherent states for isospectral oscillator Hamiltonians

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 considered.

Journal of Physics A Mathematical and General•May 21, 1994•95 citations

Generalized coherent states for a generalization of the harmonic oscillator

Won Sang Chung

Generalized coherent states for a family of iso-spectral oscillator Hamiltonian are constructed from a suitable choice of the step operators of the harmonic oscillator. We investigate the non-classical property of these coherent states.

Modern Physics Letters A•Apr 15, 2015•1 citation

Coherent states for the relativistic harmonic oscillator

V. Aldaya, Julio Guerrero

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

•Jan 1, 1995•0 citations

Inverse operators in Fock space studied via a coherent-state approach

Fan Hong‐Yi

The Fock representation of the inverse of harmonic-oscillator creation and annihilation operators [see, e.g., C. L. Mehta, Anil K. Roy, and G. M. Saxena, Phys. Rev. A 46, 1565 (1992)] are naturally derived via a coherent-state approach. The completeness relation of Fock space is reexpressed by the inverse operators. Applications of the inverse operators in studying the phase operators and in normally ordering some operators are given.

Physical Review A•May 1, 1993•29 citations

A new class of coherent states and it's properties.

Abdlgader Mohamed

The study of coherent states (CS) for a quantum mechanical system has \nreceived a lot of attention. The definition, applications, generalizations of \nsuch states have been the subject of work by researchers. A common starting \npoint of all these approaches is the observation of properties of the original \nCS for the harmonic oscillator. It is well-known that they are described \nequivalently as (a) eigenstates of the usual annihilation operator, (b) from \na displacement operator acting on a fundamental state and (c) as minimum \nuncertainty states. What we observe in the different generalizations proposed \nis that the preceding definitions are no longer equivalent and only some of \nthe properties of the harmonic oscillator CS are preserved. \nIn this thesis we propose to study a new class of coherent states and \nits properties. We note that in one example our CS coincide with the ones \nproposed by Glauber where a set of three requirements for such states has \nbeen imposed. The set of our generalized coherent states remains invariant \nunder the corresponding time evolution and this property is called temporal \nstability. Secondly, there is no state which is orthogonal to all coherent states (the coherent states form a total set). The third property is that we \nget all coherent states by acting on one of these states [¿fiducial vector¿] with \noperators. They are highly non-classical states, in the sense that in general, \ntheir Bargmann functions have zeros which are related to negative regions of \ntheir Wigner functions. Examples of these coherent states with Bargmann \nfunction that involve the Gamma and also the Riemann ¿ functions are represented. \nThe zeros of these Bargmann functions and the paths of the zeros \nduring time evolution are also studied.

•Jan 1, 2011•0 citations

Ladder operators for isospectral oscillators

S. Seshadri, V. Balakrishnan, S. Lakshmibala

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed “distorted” Heisenberg algebra (including the q-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the nonlocal operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock–Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.

arXiv:quant-ph/9905100•Journal of Mathematical Physics•Feb 1, 1998•11 citations
Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.
The study of coherent states (CS) for a quantum mechanical system has \nreceived a lot of attention. The definition, applications, generalizations of \nsuch states have been the subject of work by researchers. A common starting \npoint of all these approaches is the observation of properties of the original \nCS for the harmonic oscillator. It is well-known that they are described \nequivalently as (a) eigenstates of the usual annihilation operator, (b) from \na displacement operator acting on a fundamental state and (c) as minimum \nuncertainty states. What we observe in the different generalizations proposed \nis that the preceding definitions are no longer equivalent and only some of \nthe properties of the harmonic oscillator CS are preserved. \nIn this thesis we propose to study a new class of coherent states and \nits properties. We note that in one example our CS coincide with the ones \nproposed by Glauber where a set of three requirements for such states has \nbeen imposed. The set of our generalized coherent states remains invariant \nunder the corresponding time evolution and this property is called temporal \nstability. Secondly, there is no state which is orthogonal to all coherent states (the coherent states form a total set). The third property is that we \nget all coherent states by acting on one of these states [¿fiducial vector¿] with \noperators. They are highly non-classical states, in the sense that in general, \ntheir Bargmann functions have zeros which are related to negative regions of \ntheir Wigner functions. Examples of these coherent states with Bargmann \nfunction that involve the Gamma and also the Riemann ¿ functions are represented. \nThe zeros of these Bargmann functions and the paths of the zeros \nduring time evolution are also studied.
We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed “distorted” Heisenberg algebra (including the q-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the nonlocal operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock–Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.