谐振子任意次幂动量算符矩阵元的计算

本文利用一维谐振子的升降算符合出了计算动量算任意次幂Ｐ＾ｋ的矩阵元及平均值通式，并建立了与坐标算符矩阵元的转换关系。     

几类粒子密度算符和粒子流密度算符的讨论

从粒子密度和粒子流密度出发,分析了几类相关的算符,讨论了它们的性质与相互关系;从具体的物理意义出发,明确了合适的粒子密度算符和粒子流密度算符的表达形式.     

曲线坐标系中相对论性动量分量的算符中会出现∑z项吗

指出相对论性动量算符＾↑p在任何坐标系中的分量，包括在曲线坐标系中的分量也是动量分量的算符，不可能出现与自旋矩阵有关的项，指出了电子自旋是轨道角动量的相对论效应的观点没有理论根据。     

复合函数算符的微商法则及其在量子物理中的应用

给出了在量子物理学、量子统计学、算符排序理论、矩阵论以及控制理论中有着重要用途的复合函数算符的一般微分法则,利用这一法则研究了Wigner算符和Weyl对应规则中的积分问题,证明了两类典型的算符恒等公式.给出了Wigner算符的有序算符内的微分形式,并得到了一些重要函数的新的微分式.最后,引入了一个参数型的Wigner算符来统一正规序、Weyl编序以及反正规序三种算符排序.     

对量子力学中角动量的一点认识

指出了角动量算符Ｊ不存在本征值和本征矢量完全集,角动量算符Ｊ不描写一个可观察量以及角动量Ｊ不宜作为整体来讨论。     

三维各向同性谐振子的径向基本算符

采用新的方法,推导出三维各向同性谐振子径向基本算符r,r,1r对本征函数的作用结果,由此得出其升降算符及其他新的公式,并证明文献[1]中的结论有误 关键词： 基本算符 升降算符 三维谐振子     

Introducing the general condition for an operator in curved space to be unitary

We investigate the general condition for an operator to be unitary. This condition is introduced according to the definition of the position operator in curved space. In a particular case, we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator. Also we introduce a universal formula for adjoint of an arbitrary linear operator. Our procedure in this paper is totally different from others, as we explore a general approach based only on the algebra of the operators. Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.     

How To Recognize The Creation Operator

We discuss three characterizations of the creation operator of diverse sort, which in this or another way refer to the commutation relation of the quantum harmonic oscillator.     

曲线坐标系中相对论性动量分量的算符中会出现Σ_z项吗

指出相对论性动量算符p^在任何坐标系中的分量 ,包括在曲线坐标系中的分量也是动量分量的算符 ,不可能出现与自旋矩阵有关的项 .指出了电子自旋是轨道角动量的相对论效应的观点没有理论根据 .     

描述高自旋弱耦合系统的广义积算符

本文提出了Z算符与角动量积算符相结合的广义积算符,用于描述高自旋弱耦合系统NMR实验谱。给出了高自旋系统在自旋耦合作用下的演变公式,Z算符在脉冲作用下的变化公式。以氘(D)为例,计算了重聚INEPT,DEPT和同核COSY实验谱,并对计算方法作了讨论。     

谐振子产生算符和湮没算符的逆算符

本引入谐振子产生算符和湮没算符的逆算符，导出它们在Ｆｏｃｋ空间的表达式，并给出了一些简单应用。     

Gazeau–Klauder coherent states examined from the viewpoint of diagonal ordering operation technique

In this paper we investigate the Gazeau–Klauder coherent states using a newly introduced diagonal ordering operation technique, in order to examine some of the properties of these coherent states. The results coincide with those obtained from other purely algebraic methods, but the calculations are greatly simplified. We apply the general theory to two cases of Gazeau–Klauder coherent states: pseudoharmonic as well as the Morse oscillators.     

Quantum Hadamard Operators and Their Decomposition Derived by Virtue of IWOP Technique

We introduce the quantum Hadamard operator in continuum state vector space and find that it can be decomposed into a single-mode squeezing operator and a position-momentum mutual transform operator. The two-mode Hadamard operator in bipartite entangled state representation is also introduced, which involves the two-mode squeezing operator and [η〉 ←→｜ξ〉 mutual transformation operator, where [η〉 and ｜ξ〉 are mutual conjugate entangled states. All the discussions are proceeded by virtue of the IWOP technique.     

Projection operator approach to the thermodynamic formalism of dynamical systems

An analytical perturbative treatment of characteristic exponents describing the fluctuations of temporal coarse-grained quantities in the context of nonlinear dynamical systems is proposed. It is based on the analysis of the resolvent of the corresponding transfer operator by a projection operator method similar to those used in statistical mechanics. Two different approximation schemes are presented and tested for the case of an exactly solvable but nontrivial model system.     

空间矩和Zernike矩亚像素边缘算子分析

讨论了空间矩、Zernike矩两个亚像素边缘算子的运行时间和定位精度。分析结果表明,Zernike具有更快的运行速度,当计算3个用于边缘定位的参数时,其运行时间较空间矩算子节约了50%。理论分析了空间矩和Zernike矩算子的关系,并推导出了两个算子边缘距离为l的差值公式。测试结果表明,当两个算子的l都限制在中心像素内时,空间矩算子的边缘厚度多达3个像素,而Zernike矩算子的边缘厚度小于1个像素,可见Zernike矩算子的定位精度为真正的亚像素级。经比较,Zernike矩算子的运行时间和定位精度均好于空间矩算子。