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量子光学学报 2024年第1期30卷 14-17页

作者：展德会范洪义武夷学院机电工程学院福建武夷山354300 中国科学技术大学材料科学与工程系安徽合肥230026

在量子光学理论计算中,经常遇到算符的正规排序和反正规排序问题,我们从双变量厄米多项式Hm,n(x,y)的母函数出发,导出两个简洁的重要的基本算符恒等式并由此可以给出一些推论公式。

关键词：双变量厄米多项式算符恒等式正规排序反正规排序

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从光的生-灭机制阐述量子力学

菏泽学院学报 2024年第2期46卷 1-11页

作者：范洪义中国科学技术大学材料科学与工程系安徽合肥230026

通过引入有序算符内的积分理论,从光子产生–湮灭的观点出发来阐述量子力学理论,显示表象的正态分布,在数学上支持量子力学的几率假设;指出如何从经典变换直接过渡到量子幺正算符,自然地引入纠缠态表象,并指出数学物理研究的新方向.

关键词：有序算符正态分布纠缠态幺正变换

Weyl-Ordered Operator Moyal Bracket by Virtue of Method of Integral Within an Weyl Ordered Product of Operators

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Communications in Theoretical Physics 2006年第2期45卷 245-248页

作者： fan hong-yi Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

The Moyal bracket is an exemplification of Weyl＇s correspondence to formulate quantum mechancis in terms of Wigner function. Here we present a formalism of Weyl-ordered operator Moyal bracket by virtue of the method... 详细信息

关键词： Weyl ordering Weyl-ordered operator Moyal bracket IWWOP method

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

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Communications in Theoretical Physics 2008年第10期50卷 935-937页

We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation t... 详细信息

关键词： new two-fold integration transform phase space Weyl ordering of operators

On Diagonal P-Representation of Superposition Field of Two Light Modes

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Communications in Theoretical Physics 2006年第5X期45卷 845-848页

作者： fan hong-yi 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

For the superposition field a^＋1＋aA^＋2 of two light modes we introduce an appropriate diagonal P-representation which is constructed on the common eigenvectors ｜z,x 〉 of （X1 -X2） and al ＋ a2, where Xi = （ai ＋ a^＋i） /√2, [ai, a^＋i] = δij. It is remarkable that ｜z, x〉make up a new quantum mechanical representation.

关键词： superposition fields diagonal P-representation coherent-entangled state representation

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

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Communications in Theoretical Physics 2008年第11期50卷 1089-1092页

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl orderedproduct of operators,i.e.,the Weyl correspondence rule can be reconstructed by classical functions' Fourier transfor-mation followed by an inverse Fourier transformation within Weyl ordering of *** an application of thisreconstruction,we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.

关键词： Weyl quantization Weyl ordering of operators angular spectrum of spherical wave

Wigner Function:from Ensemble Average of Density Operator to Its One Matrix Element in Entangled Pure States

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Communications in Theoretical Physics 2002年第5期38卷 533-536页

作者： fan hong-yi Department of Physics Shanghai Jiao Tong UniversityShanghai 200030China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

We show that the Wigner function W = Tr(△ρ) (an ensemble average of the density operator ρ, △ is theWigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting fromquantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangledstates are defined in the enlarged Fock space with a fictitious freedom.

关键词： Wigner function, ensemble average of density operator, matrix element in entangled pure states

A New Differential Formula About Product of Polynomials and Its Application in Multi-electron State Physics

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Communications in Theoretical Physics 2006年第3X期46卷 419-422页

We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ＂related to Laughlin wave function＂. The entangled state representatio... 详细信息

关键词： new differential formula product of polynomials multi-electron state

“Angle” Operator Conjugate to Photon’s Intrinsic Angular Momentum

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Chinese Physics Letters 2001年第7期18卷 857-859页

作者： fan hong-yi Department of Applied Physics Shanghai Jiao Tong UniversityShanghai 200030 Department of Material Science and Engineering University of Science and Technology of ChinaHefei 230026

We find the correct“angle”operator conjugate to the intrinsic angular momentum of tne photon by introducing a suitable representation which involves both left-handed and right-handed polarization photon operators.

关键词： conjugate Conjugate momentum

Three-Particle Entangled States of Continuum Variables

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Chinese Physics Letters 2001年第10期18卷 1308-1311页

作者： fan hong-yi Department of Physics Shanghai Jiao Tong UniversityShanghai 200030 Department of Material Science and Engineering University of Science and Technology of ChinaHefei 230026

We introduce the three-particle entangled state of continu um variables, which is a generalization of Greenberger Horne-Zeilinger entangled states composed of discrete states. The completeness relation and partly non-orthonormal property of such states are proven. Their Schmidt decomposition is manifestly shown and their generation is briefly discussed.

关键词： states generalization property