坐标表象与任意力学量表象的关系

通过讨论坐标表象和任意力学量表象的关系,首先分析了具有连续本征值的算符本征函数δ函数归一化的由来,在此基础上研究得出一个结论,即任意力学量算符在坐标表象中的本征函数和坐标算符在任意力学量表象中的本征函数互为共轭复数,又根据这个结论对本征函数封闭性的物理意义做了一种新的解释.     

非共振相互作用系统中密度算符间距的演化

考虑到失谐量和原子初始相干性,给出了任意初态分布的二能级原子与任意单模场相互作用的密度算符间距的一般表达式.着重讨论了一个任意态分布的二能级原子与相干态光场相互作用时失谐量对密度算符间距演化的影响.结果表明：密度算符间距明显地依赖于失谐量的取值. 关键词：     

四粒子任意纠缠态的控制隐形传输

隐形传送体系的总量子态的实质是完备基展开与变换算符的线性叠加,若变换算符可逆,且为幺正算符,则进行相应的逆幺正变换操作即可实现量子态的隐形传送;若变换算符不可逆,则不能实现任意量子态的隐形传送.本文由变换算符给出四粒子任意纠缠态的控制隐形传输的理论分析,给出控制方对拥有的粒子进行Hadamard门变换与不进行.Hadamard门变换的解释.     

量子隐形传送态的正交完备基展开与算符变换

由波函数的叠加原理与变换算符出发，以三对任意纠缠的粒子作为量子通道对一个任意的三粒子态实现隐形传送为例，将体系的总量子态按Bell基展开，理论上接受者只需直接对自己拥有的粒子进行相应的变换，可使这三粒子恢复原始量子态，从而实现任意量子态的隐形传送.给出了变换算符与实际操作算符的联系.进一步可得出变换算符可逆是成功实现量子隐形传送的必要条件. 关键词： Bell基展开 隐形传送 变换算符     

算符二次量子化形式的一种导出方式

首先通过单体算符在粒子数表象下的形式得到单粒子跃迁算符(定义为粒子产生湮没算符的乘积,即a+iaj)的具体展开式,同时给出它与产生湮没算符的对易关系,然后以此为基础,在不区分全同粒子系统的统计学性质的情况下,简洁地得到二体算符和任意n体算符的二次量子化形式.     

体积算符对任意价顶角的本征作用与本征值谱

利用体积算符所含抓三元组对自旋网任意价顶角中圈线作用的反称化和双元恒等式，证明了这种作用均为本征作用，本征值为-2.用代数方法给出了对任意价顶角求体积算符本征值的系统程式，得到了普遍情况下的3，4，5和6顶角体积本征值的具体代数表式. 关键词： 体积算符 任意价顶角 本征作用证明 本征值谱     

三类互不等价的压缩算符

构造了三类压缩算符,将其中任何一类作用于相干态,均可得到具有任意压缩度的理想压缩态.熟知的压缩算符是其中一类的特殊情况.三类算符互不等价,即不能通过线性正则变换互相转化.     

压缩算符在自由标量场理论中的推广

引入了一种在量子场论中构造压缩算符的办法:考虑两个具有不同质量的同一标量场的自由哈密顿量,通过博戈留波夫变换,导出广义压缩算符,该算符把一个基态映射到另一个。该算符作用的有效性分别在量子场论的狄拉克表象和薛定谔泛函表象中得到了验证。我们相信,在任意实标量场理论中,只要存在两组以线性变换联系起来的生成湮灭算符,压缩算符就被类似的方法找到。     

各向同性谐振子径向基本算符的应用

利用基本算符D/Dρ,ρ,1/ρ对本征函数RNL的递推关系和任意力学量算符对函数RNL的作用结果,容易求得力学量的矩阵元和平均值等。     

相对论粒子的自旋算符

发展了关于相对论态自旋算符的系统理论.考虑了具有非零静质量的粒子情况.对带自旋的相对论粒子,通常的自旋算符需换为相对论的自旋算符.在Poincar啨群不可约表示的框架里,构造了适用于粒子任意正则态的自旋算符,称为运动自旋.本文的讨论限于量子力学.随后将在量子场论中对此作进一步深入研究.     

The symplectic eigenfunction expansion theorem and its application to the plate bending equation

This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.     

Tensor operators for quantum algebras

Tensor operators are discussed for Hopf algebras and, in particular, for a quantum (q-deformed) algebraUq(g), whereg is any simple finite-dimensional or affine Lie algebra. These operators are defined via an adjoint action in a Hopf algebra. There are two types of the tensor operators which correspond to two coproducts in the Hopf algebra. In the case of tensor products of two tensor operators one can obtain 8 types of the tensor operators and so on. We prove the relations which can be a basis for a proof of the Wigner-Eckart theorem for the Hopf algebras. It is also shown that in the case ofUq(g) a scalar operator can be differed from an invariant operator but atq=1 these operators coincide. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. Supported by Russian Foundation for Fundamental Research, grant 99-01-01163, and by INTAS-00-00055.     

On the existence of joint probability distributions for arbitrary incompatible observables in quantum mechanics

It is shown that for any two operators A and C on any Hilbert space H it is possible to construct infinitely many positive operator valued measures which can serve as joint probability distributions for A and C.     

Folded diagrams

The Morita-Brandow folded diagrams are derived from a time-dependent point of view. The effective interaction in the model space is energy-independent, contains only linked clusters, and can easily be made Hermitian. Even then, it is still highly arbitrary. For each choice of effective interaction, rules are given for the calculation of effective operators, such that the matrix element of any effective operator between any two model states equals the matrix element of the true operator between the corresponding true states. Examples of folded diagrams are given and methods for calculating them are explained. Examples of effective operators are also given, including the effective spectroscopic amplitude, whose square is the spectroscopic factor of one-nucleon transfer reactions.     

Einstein–Podolski–Rosen paradox,non-commuting operator,complete wavefunction and entanglement

Einstein, Podolski and Rosen (EPR) have shown that any wavefunction (subject to the Schrödinger equation) can describe the physical reality completely, and any two observables associated with two non-commuting operators can have simultaneous reality. In contrast, quantum theory claims that the wavefunction can capture the physical reality completely, and the physical quantities associated with two non-commuting operators cannot have simultaneous reality. The above contradiction is known as the EPR paradox. Here, we unambiguously expose that there is a hidden assumption made by EPR, which gives rise to this famous paradox. Putting the assumption right this time leads us not to the paradox, but only reinforces the correctness of the quantum theory. However, it is shown here that the entanglement phenomenon between two physically separated particles (they were entangled prior to separation) can only be proven to exist with a ‘proper’ measurement.     

Intertwining operator realization of non-relativistic holography

We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory (without specifying any action). Further we show that these operators and the bulk-to-boundary operators are intertwining operators. In analogy to the relativistic case, we show that each bulk field has two boundary fields with conjugated conformal weights. These fields are related by another intertwining operator given by a two-point function on the boundary. Analogously to the relativistic result of Klebanov–Witten we give the conditions when both boundary fields are physical. Finally, we recover in our formalism earlier non-relativistic results for scalar fields by Son and others.     

Scasimir Operator,Scentre and Representations of Uq(osp(1|2))

Recently, Borchers has shown that in a theory of local observables, certain unitary and antiunitary operators, which are obtained from an elementary construction suggested by Bisognano and Wichmann, have the same commutation relations with translation operators as Lorentz boosts and P₁CT operators would have, respectively. It is concluded from this that as soon as the operators considered implement any symmetry, this symmetry can be fixed up to at most some translation. As a symmetry, any unitary or antiunitary operator is admitted under whose adjoint action any algebra of local observables is mapped onto an algebra which can be localized somewhere in Minkowski space.     

Decay of correlations in Fermi systems at nonzero temperature

The locality of correlation functions is considered for Fermi systems at nonzero temperature. We show that for all short-range, lattice Hamiltonians, the correlation function of any two fermionic operators decays exponentially with a correlation length which is of order the inverse temperature for small temperature. We discuss applications to numerical simulation of quantum systems at nonzero temperature.