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

Chinese Physics Letters

Introduction and Applications of a Generalized Intermediate Entangled State Representation

Pang Qian-Jun

Published Sep 22, 2005• 1 citation
Publisher

Abstract

We introduce a generalized intermediate entangled state representation |β⟩ Λ to study the energy spectrum of an electron in a uniform magnetic field and a harmonic potential through algebraic calculation. We find that the degeneracy of the energy levels is disappeared due to the existence of the additional potential. We make it clear that the eigenfunction is just the expression of eigenvector, defined in n Fock space, in |β⟩ Λ representation.

DOI
10.1088/0256-307x/22/10/004

Related papers

Properties and Application of Intermediate Entangled State Representation

Pang Qian-Jun

We introduce the intermediate entangled state |α⟩ and discuss its properties of |α⟩ λ,ν . We obtain the expression of the two-mode Wigner operator in the |α⟩ λ,ν representation. We find that the projection operator |α⟩ λ,ν λ,ν ⟨α| is just the Radon transformation of the two-mode Wigner operator. Using the |α⟩ λ,ν representation, we successfully obtain the eigenvalues and eigenvectors of a bipartite system coupled in a quite complicated way.

Chinese Physics Letters•May 25, 2005•4 citations

APPLICATION OF INTERMEDIATE ENTANGLED STATE REPRESENTATION ON SOLVING COUPLED OSCILLATOR

QIANJUN PANG

Through introducing an intermediate entangled state representation |β〉λν interpolating the entangled states |η〉 and |ξ〉, the eigenvalues and eigenvectors of a bipartite fully-coupled oscillators are discussed within some different situations.

Modern Physics Letters B•Nov 28, 2005•1 citation

Energy Spectrum of a Bipartite Complicated-Coupled-Oscillator System

Pang Qian-Jun

We present a general discussion on the eigenstate problem of a bipartite complicated-coupled-oscillator system. By use of a generalized intermediate entangled state representation, the eigenvalue and eigenfunction of Hamiltonian are analytically obtained. As its application, we obtain the energy spectrum for two special situations of Hamiltonian.

Communications in Theoretical Physics•Mar 1, 2006•0 citations

Deriving the eigenvector of the operator λ■+μ■ by|x〉

Hongqi Li

By the representation of the coordinate eigenvector |x〉 in the Fock space,the eigenvector |ψ〉 of the operator λ■+μ■ is derived and its orthogonal relation is also proved.These results show that the eigenvector |ψ〉 satisfies the completeness and the orthogonal relations.Therefore,this eigenvector |ψ〉 can be qualified for a representation in quantum mechanics.When λ=1 and μ= 0,the eigenvector |ψ〉 evolves into the coordinate eigenvector |x〉;while λ=0 and μ =1,the |ψ〉 reduces to the momentum eigenvector |p〉.Therefore,the representation consisted by the eigenvectors |ψ〉 is an intermediate representation between the coordinate representation and the momentum representation.

College Physics•Jan 1, 2010•0 citations

THE APPLICATION AND CHARACTERISTICS OF THE COHERENT ENTANGLED STATE |β, x〉

YUN-HAI ZHANG, Xing-Lei Xu, Shi-Min Xu +1 more

The coherent entangled state |β, x〉 is proposed in Fock space, which exhibits both the properties of the coherent and entangled states. The |β, x〉 makes up a new quantum mechanical representation, and the completeness relation of |β, x〉 is proved by virtue of the technique of integral within an ordered product of operators. The corresponding Schmidt decomposition of |β, x〉 is investigated. Furthermore, a feasible experimental scheme of |β, x〉 is presented, and generalized P-representation is constructed in the coherent entangled state |β, x〉.

International Journal of Modern Physics B•Apr 6, 2011•0 citations

New Two-Mode Coherent-Intermediate-Entangled State and Its Squeezing Operator

Shi-Min Xu, Xing-Lei Xu, Hongqi Li

The coherent-intermediate-entangled state |α, x ⟩ λ,ν is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The |α, x ⟩ λ,ν makes up a new quantum mechanical representation, and the completeness relation of |α, x ⟩ λ,ν is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state |α, x ⟩ λ,ν and the Schmidt decomposition of |α, x ⟩ λ,ν is investigated.

Communications in Theoretical Physics•Nov 1, 2009•1 citation
We introduce a generalized intermediate entangled state representation |β⟩ Λ to study the energy spectrum of an electron in a uniform magnetic field and a harmonic potential through algebraic calculation. We find that the degeneracy of the energy levels is disappeared due to the existence of the additional potential. We make it clear that the eigenfunction is just the expression of eigenvector, defined in n Fock space, in |β⟩ Λ representation.
By the representation of the coordinate eigenvector |x〉 in the Fock space,the eigenvector |ψ〉 of the operator λ■+μ■ is derived and its orthogonal relation is also proved.These results show that the eigenvector |ψ〉 satisfies the completeness and the orthogonal relations.Therefore,this eigenvector |ψ〉 can be qualified for a representation in quantum mechanics.When λ=1 and μ= 0,the eigenvector |ψ〉 evolves into the coordinate eigenvector |x〉;while λ=0 and μ =1,the |ψ〉 reduces to the momentum eigenvector |p〉.Therefore,the representation consisted by the eigenvectors |ψ〉 is an intermediate representation between the coordinate representation and the momentum representation.
The coherent entangled state |β, x〉 is proposed in Fock space, which exhibits both the properties of the coherent and entangled states. The |β, x〉 makes up a new quantum mechanical representation, and the completeness relation of |β, x〉 is proved by virtue of the technique of integral within an ordered product of operators. The corresponding Schmidt decomposition of |β, x〉 is investigated. Furthermore, a feasible experimental scheme of |β, x〉 is presented, and generalized P-representation is constructed in the coherent entangled state |β, x〉.
The coherent-intermediate-entangled state |α, x ⟩ λ,ν is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The |α, x ⟩ λ,ν makes up a new quantum mechanical representation, and the completeness relation of |α, x ⟩ λ,ν is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state |α, x ⟩ λ,ν and the Schmidt decomposition of |α, x ⟩ λ,ν is investigated.