CG系数的计算

从角动量的对易关系出发,直接计算了两个角动量耦合的Clebsch-Gordan系数.     

利用Gel'fand基计算SU(3)Clebsch-Gordan系数的Mathematica软件

利用Gel'fand基和对相因子约定的分析,编写了一个计算SU(3)Clebsch-Gordan(C-G)系数的Mathematica软件。其计算结果与广义Condon-Shortley相因子约定下的结果一致。     

SU_3群的多项式基底及其Clebsch-Gordan系数的明显表达式

利用对称性与Young图在多项式空间上构成了SU_n群的不可约表示及积表示的完全基底,从而不但区分了非单纯权也区分了积表示的非简单可约性,并在此基础上用构成不变量法得到SU_3群的Clebsch-Gordan系数的明显表达式     

SU3群的多项式基底及其Clebsch-Gordan系数的明显表达式

利用对称性与Young图在多项式空间上构成了SU_n群的不可约表示及积表示的完全基底,从而不但区分了非单纯权也区分了积表示的非简单可约性,并在此基础上用构成不变量法得到SU₃群的Clebsch-Gordan系数的明显表达式     

SU3群不可约表示直乘中的不可约表示及其重数

本文运用Racah-Speier定理研究了SU₃群的Clebsch-Gordan级数.,建立了计算这个级数中的不可约表示及其重数的普遍公式。这个公式对具体计算是非常简单而有效的。可以运用这个公式去分析SU₃的Clebsch-Gordan级数中重数的分布规律,以及确定SU₃的Wigner算符的零空间,后者对计算有重数情形下的Wigner系数是重要的。     

Clebsch-Gordan系数的矩阵求法

在考虑两角动量耦合时,我们常要用到两种表象──耦合表象和非耦合表象.两表象间通过Clebsch-Gordan系数(以下简称C-G系数)相互联系.本文提出一种用矩阵力学求解C-G系数的方法. 设J=J1+J2,不难得出 这样便可以求得矩阵J2,Jz,将该两矩阵的共同本征矢在无耦合表象的基矢｜jm1j2m2>中展开,则展开系数即为C-G系数. 以上所述也可用矩阵直积的形式简单地表示出来.设(2j1+1)(2j2+1)维空间中两个因子空间V(j1)和V(j2)的基矢选取为:V(ji):｜j1j1>,｜j1j1-1>……匕一人>;V’“’:U小>,U小一1>@…··u。一人>而无耦合表象基矢选为中。,。分别…     

远紫外高光谱成像光谱仪的辐射定标技术

利用紫外恒星对远紫外高光谱成像光谱仪进行在轨定标是实现高精度定量遥感的重要步骤。然而,在上述过程中,在轨定标系数无法直接用于目标反演。因此,转换在轨定标系数对提升仪器在轨定标精度具有重要意义。推导了定标系数的转换过程,给出了新的定标系数方程,并利用研制的仪器开展了相关验证实验。结果表明,利用修正后的定标系数进行目标反演,可将反演精度提升40%。     

用激光干涉法测量电致伸缩系数

简述了利用迈克耳孙干涉仪测量电致伸缩系数的原理,介绍了测量电致伸缩系数的方法,给出了同心圆干涉条纹的圈数与所加电压的关系以及利用线性回归法求准线性区域的电致伸缩系数的测量结果.     

热光系数与长周期光纤光栅的温度灵敏度研究

利用受温度影响的光纤的本征方程和相位匹配条件,从理论上研究了长周期光纤光栅(LPFGs)的温度响应特性,给出了LPFGs的温度灵敏度的解析表达式。对利用低模序包层模的LPFG进行了实验研究。结果表明,利用不同包层模的LPFGs具有不同的温度灵敏度。分析了光纤的材料热光系数和模的热光系数的差别。单模光纤导模的热光系数接近纤芯的材料热光系数,而包层模的热光系数比包层的材料热光系数大,模序越大,其值越大。适当调整纤芯和包层的热光系数,并选用不同的包层模,可以得到对温度灵敏或不灵敏的LPFGs。     

落球法液体粘滞系数测定仪的改造研究

将两种测量液体粘滞系数的原理进行了介绍,对利用这两种原理测量液体粘滞系数的仪器进行了改造,将两者组合为一套仪器,实现了一套仪器两种方法测量液体粘滞系数的构想,并提高了利用多管法原理仪器的测量精度。     

Clebsch-Gordan coefficients for the Poincaré group

All Clebsch-Gordan coefficients for the Poincaré group are calculated by a simple global method.     

Beyond Euler angles: exploiting the angle-axis parametrization in a multipole expansion of the rotation operator

Euler angles (alpha,beta,gamma) are cumbersome from a computational point of view, and their link to experimental parameters is oblique. The angle-axis {Phi, n} parametrization, especially in the form of quaternions (or Euler-Rodrigues parameters), has served as the most promising alternative, and they have enjoyed considerable success in rf pulse design and optimization. We focus on the benefits of angle-axis parameters by considering a multipole operator expansion of the rotation operator D(Phi, n), and a Clebsch-Gordan expansion of the rotation matrices D(MM')(J)(Phi, n). Each of the coefficients in the Clebsch-Gordan expansion is proportional to the product of a spherical harmonic of the vector n specifying the axis of rotation, Y(lambdamu)(n), with a fixed function of the rotation angle Phi, a Gegenbauer polynomial C(2J-lambda)(lambda+1)(cosPhi/2). Several application examples demonstrate that this Clebsch-Gordan expansion gives easy and direct access to many of the parameters of experimental interest, including coherence order changes (isolated in the Clebsch-Gordan coefficients), and rotation angle (isolated in the Gegenbauer polynomials).     

Relation between the parabolic and spherical eigenfunctions of hydrogen

It is shown that the transformation coefficients relating the eigenfunctions of the Kepler problem in parabolic and spherical coordinates respectively are the normalized Clebsch-Gordan coefficients.     

Clebsch-Gordan Coefficients,Racah Coefficients and Braiding Fusion of Quantum sl(2) Enveloping Algebra (I)

Quantum Clebsch-Gordan coefficients and the first type quantum Racah coefficients of quantum sl(2) enveloping algebra are given explicitly. The quantum 3-j and 6-j symbols, similar to those in the theory of angular momentum are abo introduced. The solution R_q^j1j2 of quantum Yang-Baxter equaton is expressed in terms of the quantum Clebsch-Gordan coefficients. It is shown that when j1=j2, R_q^jj is just the same as R_AW^j matrix obtained by Akutsu and Wadati for the representation of the braid group. The second type quantum Racah coefficients, which are the solutions of the face models, are also computed explicitly and related to the first type quantum Racah coefficients. The famous pentagonal relation is proved from the formula between two quantum Racah coefficients. The graphical representation of those formulas is discussed.     

Integration over the group space of SUq(2), Clebsch-Gordan coefficients, and related identities

We calculate the Clebsch-Gordan coefficients of SUq(2) by a Woronowicz integration over the group manifold and obtain a representation differing from that reached by working with theq-group algebra. These apparently different results must agree, however, and their equivalence implies aq-identity. On lettingq = 1, we shall obtain two results of different structures for the Clebsch-Gordan coefficients of SU(2) and their equivalence similarly implies an identity among the usual binomial coefficients. With the same approach, one may extend the Woronowicz integral of the product of two irreducible representations to products of many irreducible representations.     

SU3羣不可约表示直乘的分解

本文利用SU₃羣无穷小算子的对易关系,求出了SU₃羣的所有不可约U表示,并导出了SU₃羣的约化系数满足的方程。作为例子,我们计算了SU₃羣的(01)×(10),(11)×(10),(11)×(11),(30)×(11)的约化系数。     

Coefficients of Clebsch-Gordan for the holomorphic discrete series

We prove a theorem for the tensor product of representations of the holomorphic discrete series analogous to the classical theorem of Clebsch-Gordan and give an asymptotic formula for corresponding coefficients of Clebsch-Gordan. For small groups we compute the coefficients explicitly.Partially supported by NSF Grant MCS 78-01826.     

A simple sum formula for Clebsch-Gordan coefficients

I derive a simple identity involving a sum of Clebsch-Gordan coefficients with zero magnetic quantum numbers.     

Clebsch-Gordan Coefficients,Racah Coefficients and Braiding Fusion of Quantum sl(2) Enveloping Algebra Ⅱ

The explicit forms of the quantum Clebsch-Gordan coefficients and the first-type quantum Racah coefficients for the quantum sl(2) enveloping algebra are computed in detail. Exact values of some coefficients are listed. An important relation, quantum Racah sum rule, is proved.