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

Journal of Physics A Mathematical and General

A q-analogue of the supersymmetric oscillator and its q-supercoherent states

Gong Ren-shan

Published Oct 7, 1994• 1 citation
Publisher

Abstract

A q-analogue of the supersymmetric oscillator is constructed out of q-boson and ordinary fermion creation and annihilation operators. q-supercoherent states are explicitly obtained for the q-deformed supersymmetric oscillator. They are shown to be eigenstates of both q-boson and fermion annihilation operators and to satisfy a completeness relation. The representation of the q-deformed superalgebra in super Bargmann-Fock space is also discussed by means of the q-supercoherent states.

DOI
10.1088/0305-4470/27/19/023

Related papers

The q -Deformation of the Superoscillators and Their q -Supercoherent States

Hao San-Ru, Wang LuYa

We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q -deformed operators, we also give the q -deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q -supercoherent states associated with the q -deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q -supercoherent states are discussed as well.

Communications in Theoretical Physics•Oct 30, 2000•0 citations

The q-superoscillators in supersymmetric quantum systems and their q-supercoherent states

Hao San-Ru, Guanghua Li, LONG JUN-YAN

In this paper, the q-deformed quantum harmonic oscillators in the supersymmetric quantum systems are introduced. The q-supercoherent states associated with the q-deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated in detail. It is shown that the q-supercoherent states are completeness. The uncertainty relations for q-supercoherent states are discussed as well.

Journal of Physics A Mathematical and General•Sep 7, 1994•1 citation

Supercoherent states

Carlos Aragone, Fredy R. Zypman

The authors present the supercoherent states. They are introduced as the eigenstates of the supersymmetric annihilation operator of the quantum mechanical supersymmetric harmonic oscillator. They have a compact expression in terms of the standard (bosonic) coherent states. For each value of the complex parameter z there are two linearly independent orthogonal supercoherent states. One of them has pure fermionic character and is the more classical, while the other is fully supersymmetric (i.e. the mean value of the Klein operator when the system is set in this state vanishes). There are no purely bosonic supercoherent states. The supercoherent fermionic states saturate both the Heisenberg uncertainty relation and the new entropic uncertainty recently introduced by Deutsch (1983), while the supersymmetric ones almost (but not exactly) make it. They give a classical (or almost classical) mean value for the energy of the system and do not spread along their time evolution.

Journal of Physics A Mathematical and General•Aug 21, 1986•57 citations

Two oscillators quantum groups and associated deformed coherent states

Nibaldo Alvarez-Moraga

Starting from a faithful five-dimensional matrix representation of the group of two independent oscillators and applying the R-matrix method we generate some classes of deformed fermionic-bosonic quantum Hopf algebras. The corresponding Lie deformed superalgebras of type I--II, obtained by duality, are computed and a realization of generators of these deformed superalgebras are given in terms of the usual fermionic and bosonic creation and annihilation operators associated to the supersymmetric harmonic oscillator. Then, a generalized deformed annihilator is construted and their eigenstates are computed giving a new class of deformed coherent states.

arXiv:math-ph/0503050•Mar 21, 2005•0 citations

The q-supercoherent states of the q-deformed su(2) superalgebra

Le-M Kuang

The q-supercoherent states associated with the q-deformed su(2) superalgebra are constructed explicitly, and their properties are investigated in detail. The completeness relation of the q-supercoherent states is proved by the use of the q-integration.

Journal of Physics A Mathematical and General•Sep 21, 1992•8 citations

Supercoherent states

B. W. Fatyga, V. Alan Kostelecký, Michael Martin Nieto +1 more

A general approach is presented for constructing coherent states for supersymmetric systems. It uses Rogers's supermanifold formulation of supergroups to extend the group-theoretic method. Supercoherent states are explicitly obtained for the supersymmetric harmonic oscillator. They are shown to be eigenstates of the supersymmetric annihilation operator and to be minimum-uncertainty states. Two more-complex situations with extended physical supersymmetries are also considered: an electron moving in a constant magnetic field, and the electron-monopole system. The supercoherent states for these systems are found using super Baker-Campbell-Hausdorff relations and their interpretation is elucidated.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Feb 15, 1991•55 citations
A q-analogue of the supersymmetric oscillator is constructed out of q-boson and ordinary fermion creation and annihilation operators. q-supercoherent states are explicitly obtained for the q-deformed supersymmetric oscillator. They are shown to be eigenstates of both q-boson and fermion annihilation operators and to satisfy a completeness relation. The representation of the q-deformed superalgebra in super Bargmann-Fock space is also discussed by means of the q-supercoherent states.
We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q -deformed operators, we also give the q -deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q -supercoherent states associated with the q -deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q -supercoherent states are discussed as well.
The authors present the supercoherent states. They are introduced as the eigenstates of the supersymmetric annihilation operator of the quantum mechanical supersymmetric harmonic oscillator. They have a compact expression in terms of the standard (bosonic) coherent states. For each value of the complex parameter z there are two linearly independent orthogonal supercoherent states. One of them has pure fermionic character and is the more classical, while the other is fully supersymmetric (i.e. the mean value of the Klein operator when the system is set in this state vanishes). There are no purely bosonic supercoherent states. The supercoherent fermionic states saturate both the Heisenberg uncertainty relation and the new entropic uncertainty recently introduced by Deutsch (1983), while the supersymmetric ones almost (but not exactly) make it. They give a classical (or almost classical) mean value for the energy of the system and do not spread along their time evolution.
Starting from a faithful five-dimensional matrix representation of the group of two independent oscillators and applying the R-matrix method we generate some classes of deformed fermionic-bosonic quantum Hopf algebras. The corresponding Lie deformed superalgebras of type I--II, obtained by duality, are computed and a realization of generators of these deformed superalgebras are given in terms of the usual fermionic and bosonic creation and annihilation operators associated to the supersymmetric harmonic oscillator. Then, a generalized deformed annihilator is construted and their eigenstates are computed giving a new class of deformed coherent states.
A general approach is presented for constructing coherent states for supersymmetric systems. It uses Rogers's supermanifold formulation of supergroups to extend the group-theoretic method. Supercoherent states are explicitly obtained for the supersymmetric harmonic oscillator. They are shown to be eigenstates of the supersymmetric annihilation operator and to be minimum-uncertainty states. Two more-complex situations with extended physical supersymmetries are also considered: an electron moving in a constant magnetic field, and the electron-monopole system. The supercoherent states for these systems are found using super Baker-Campbell-Hausdorff relations and their interpretation is elucidated.