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New Approach for Calculating Tomograms of Quantum States by Virtue of the IWOP Technique

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Communications in Theoretical Physics 2007年第3期47卷 431-436页

We show that for tomographic approach there exist two mutual conjugate quantum states [p,σ, τ） and [x,μ, ν）（named the intermediate coordinate-momentum representation）, and the two Radon transforms of the Wigner operator are just the pure-state density matrices [p）σ1τσ1τ （p｜ and （p）λ,ν,λ,ν,（x｜ respectively. As a result, the tomogram of quantum states can be considered as the module-square of the states＇ wave function in these two representations. Throughout the paper we fully employ the technique of integration within an ordered product of operators. In this way we establish a new convenient formalism of quantum tomogram.

关键词： tomogram intermediate coordinate-momentum representation

On Quantum Mechanical Hankel Transform and Its Applications

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Communications in Theoretical Physics 2007年第2X期48卷 304-308页

作者： FAN Hong-Yi wang ji-suo Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Physics Liaocheng University Liaocheng 252059 China

Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications.

关键词： quantum mechanical Hankel transform entangled state integration equation

On Fermionic Entangled State Representation and Fermionic Entangled Wigner Operator

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Communications in Theoretical Physics 2007年第2X期48卷 245-248页

By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product （IWOP） of Fermi operators is used in our discussion.

关键词： fermionic entangled state fermionic Wigner sperator

Analogue Between Dynamic Hamiltonian-Operators of a Mesoscopic Ring Carrying Persistent Current and a Josephson Junction

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Communications in Theoretical Physics 2006年第5X期46卷 935-937页

作者： FAN Hong-Yi wang ji-suo Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Materials Science and Engineering University of Science and Technology of China Hefei 230026 China Department of Physics Liaocheng University Liaocheng 252059 China

By making the analogy between the operator Hamiltonians of a mesoscopic ring carrying the persistent current and a Josephson junction we have introduced a phase operator and entangled state representation to establish... 详细信息

关键词： phase operator for mesoscopic ring Josephson junction persistent current entangled state

On Bosonic Magnetic Flux Operator and Bosonic Faraday Operator Formula

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Communications in Theoretical Physics 2007年第6期47卷 1010-1012页

作者： FAN Hong-Yi wang Tong-Tong wang ji-suo Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China Department of Physics Liaocheng University Liaocheng 252059 China

In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators＇ commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.

关键词： magneticflux operator Faraday operator mesoscopic Josephson junction LC mesoscopic circuit entangled state representation

Two-Mode Excited Squeezed Vacuum State and Its Properties

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Communications in Theoretical Physics 2008年第5期49卷 1299-1304页

作者： MENG Xiang-Guo wang ji-suo LIANG Bao-Long Department of Physics Liaocheng University Liaocheng 252059 China

In this paper, the two-mode excited squeezed vacuum state （TESVS） is studied by using the statistical method. By calculating the normalization of the TESVS, a new form of Jacobi polynomials and some new identities are obtained. The photon number distribution of the TESVS is given and it is a simple form of Jacobi polynomials. Using the entangled state representation of Wigner operator, the Wigner function of the TESVS is obtainded and the variations of the Wigner function with the parameters m, n, and r are discussed. Here from the phase space point of view the TESVS can be well interpreted and described.

关键词： two-mode excited squeezed vacuum state photon number distribution Wigner function entangled state representation

Some Properties of Two-mode Displaced Excited Squeezed Vacuum States

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Communications in Theoretical Physics 2009年第9期52卷 493-499页

作者： MENG Xiang-Guo wang ji-suo LIANG Bao-Long Department of Physics Liaocheng University Liaocheng 252059 China

In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are *** the entangled state representation and Weyl ordering formof the Wigner operator,the Wigner functions of TDESVS are obtained and the variations of Wigner functions withthe parameters m,n and r are ***,two marginal distributions of Wigner functions of TDESVS areobtained,which exhibit some entangled properties of the two-particle's system in TDESVS.

关键词： two-mode displaced excited squeezed vacuum state Weyl ordering Wigner function marginal distribution entangled state representation

Normalized Excited Squeezed Vacuum State and Its Applications

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Communications in Theoretical Physics 2007年第5期47卷 927-932页

作者： MENG Xiang-Guo wang ji-suo LIANG Bao-Long Department of Physics Liaocheng University Liaocheng 252059 China

By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state （ESVS）, the normalized ESVS is obtained. We find that its normalization constants obtained via two new methods are uniform and a new form which is different from the result obtained by Zhang and Fan [Phys. Lett. A 165 （1992） 14]. By virtue of the normalization constant of the ESVS and the intermediate coordinate-momentum representation, the tomogram of the normalized ESVS and some useful formulae are derived.

关键词： ESVS technique of integration within an ordered product of operators intermediate coordinate- momentum representation generating function

Husimi Functions of Excited Squeezed Vacuum States

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Communications in Theoretical Physics 2009年第9期52卷 487-492页

作者： MENG Xiang-Guo wang ji-suo LIANG Bao-Long Department of Physics Liaocheng University Liaocheng 252059 China

Based on the Husimi operator in pure state form introduced by Fan et al,which is a squeezed coherentstate projector,and the technique of integration within an ordered product (IWOP) of operators,as well as the entangledstate representations,we obtain the Husimi functions of the excited squeezed vacuum states (ESVS) and two marginaldistributions of the Husimi functions of the ESVS.

关键词： excited squeezed vacuum state IWOP technique entangled state representation Husimi operator Husimi function marginal distribution