电多极矩跃迁选择定则的对称分析

只有由群的对称性才可能导出每个不可约表示的对称性波函数, 即对称化基函数.也只有由群的对称性才可能导出电子状态跃迁的最一般选择定则 , 即电偶极跃迁E1, 电四极跃迁E2 和 电八极跃迁E3跃迁的选择原则. 本文以 和 为例, 导出电多积跃迁的选择原则. 角动量的选择定则只是特例. 并用方法SAC-CI/6-31G 计算了 H2O和 CC的基态以及其激发态的激发能和振子强度.本文只适合单光子过程. 计算都与理论相合.     

电多极矩跃迁选择定则的对称分析

只有由群的对称性才可能导出每个不可约表示的对称性波函数, 即对称化基函数.也只有由群的对称性才可能导出电子状态跃迁的最一般选择定则 , 即电偶极跃迁E1, 电四极跃迁E2 和 电八极跃迁E3跃迁的选择原则. 本文以 和 为例, 导出电多积跃迁的选择原则. 角动量的选择定则只是特例. 并用方法SAC-CI/6-31G 计算了 H2O和 CC的基态以及其激发态的激发能和振子强度.本文只适合单光子过程. 计算都与理论相合.     

含有五度旋转轴点群的超拉曼张量的计算

超拉曼散射涉及晶格振动, 因此它需要由动态张量来描述。根据坐标积与张量元在对称操作下的变换形式相同的原理, 通过C语言编程, 计算了属于不同不可约表示的动态张量, 并列出了含有五度旋转轴点群的三阶超拉曼张量。     

三粒子系统的物理基

本文利用SO(6)和SU(4)局部同构性质以及SU(3)群的正则子群链与物理子群链之间的变换系数, 构造出了三个全同粒子系统内部的物理基, 并指出这个基与Aguila的超球函数基是一致的.     

基于坐标表象的脊波变换研究

在小波变换量子力学机制的启发下, 通过采用Fock空间里双模坐标本征态改写经典Ridgelet变换, 定义了量子光学态的Ridgelet变换. 然后利用IWOP技术给出不对称积分算符的显式, 并推导出了两个有用的双模算符正规乘积公式. 在此基础上, 通过选取双模“墨西哥帽”母小波函数, 分析了相干态、特殊压缩相干态、中介纠缠态表象的Ridgelet变换. 关键词： IWOP技术 Ridgelet变换 相干态     

I~N电子组态谱项结构的U群方法

多电子原子或离子的光谱理论中,一个很重要的问题就是确定由于电子间相互作用所形成的光谱项。通常采用轨道角动量耦合,自旋角动量耦合以及泡里原理来确定.当电子数N和轨道角动量量子数l大时,要经过冗长而仔细的运算才能确定下来,相当麻烦。本文利用U群方法,给出确定l~N电子组态光谱项的一般方法,大大简化了程序和工作量。首先把U_(2l 1)群的不可约表示的基直接和l~N电子组态的光谱结构联系起来,并引入了不可约表示的分解规则,及给出单列表示相应光谱项的计算方法。使计算程序标准化。     

相干态的小波变换

根据小波变换的量子力学机理, 通过选取不同的系数, 构造出两组新的母小波函数. 在此基础上, 利用正规乘积内积分技术, 推导出相干态和粒子数态的小波变换, 并数值模拟出它们的小波变换图谱.     

一种基于压缩感知的三维导体目标电磁散射问题的快速求解方法

提出了一种将压缩感知和特征基函数结合的方法来计算三维导体目标的雷达散射截面.利用压缩感知理论,将随机选择的矩量法阻抗矩阵作为测量矩阵,将激励电压视为测量值,然后再用恢复算法可实现二维或二维半目标感应电流的求解.对于三维导体目标,使用Rao-Wilton-Glisson基函数表示的感应电流在常用的离散余弦变换基、小波基等稀疏基上不稀疏.为此,本文将计算出的目标特征基函数作为稀疏基,用广义正交匹配追踪算法作为恢复算法来加速恢复过程,并应用到三维导体目标的雷达散射截面计算中.数值结果证明了本文方法的准确性与高效性.     

PrP_5O_(14)晶体中Pr~(3 )离子的晶场参数和能级

本文在C_(2v)群近似下,以点群的不可约表示基矢为波函数,计算了PrP_5O_(14)晶体中Pr~(3 )的晶场参数,Racah参数,组态相互作用参数,自旋-轨道相互作用参数.计算中考虑了J混淆和J不混淆两种情况.计算了J混淆情况的能级,并指派了不可约表示,计算和实验能级符合较好.     

SF_6分子最高占据轨道对称性的判断

量化计算是理论研究分子的重要手段,对于具有高对称群的分子,采用子群计算是常用的方法.分子的电子态或分子轨道等的对称性在子群的表示中会出现重迭,从而不能从子群的结果直接给出电子态或分子轨道对称性的归属.本文以如何判断SF6基态1 A_(1g)的电子组态中最高占据轨道的对称性为例来解决这个问题.针对某些文献中的SF6基态1 A1g的电子组态中,最高占据轨道对称性是T_(1g)却写成T_(2g)的问题,采用Molpro量化计算软件,对SF6基态的平衡结构,进行了HF/6-311G*计算,得到了能量三重简并的最高占据轨道的函数表达式,进而运用O_h群的对称操作作用在三个轨道函数上,得到各操作的矩阵表示,于是得到特征标,最后确定了最高占据轨道为T_(1g)对称性.     

On axially-symmetric finite-energy monopole configurations

Axially symmetric finite energy monopole configurations are investigated for the gauge group SO(3) with the Higgs field in the adjoint representation. To avoid the complications due to gauge freedom gauge invariant fields are introduced and used throughout. From topological and continuity considerations it is argued that the only regular axially symmetric magnetic charge distributions permitted are isolated charges of uniform strength and alternate sign located along the axis of symmetry. In particular, if there is only one sign, the magnetic charge must be located at a single point. For a zero Higgs potential the minimal energy (first order Bogomolny) field equations take a simple form when written in terms of the gauge-invariant fields. In general, there are nine equations for nine (axially symmetric) fields, but these reduce to five equations for five fields if a further symmetry (invariance under reflexions in planes through the axis of symmetry) is imposed. Remarkably, four of the equations are the same whether the reflexion symmetry is imposed or not, and these four equations can be completely solved in terms of a master potential. From these and the remaining equations (just one in the case of mirror symmetry) the asymptotic behaviour of the functions at large distances and in the neighbourhood of the origin (the location of the charge) is obtained and studied in some detail.     

The Hidden Symmetries and Their Algebraic Structure of the Static Axially Symmetric SDYM Fields

A new explicit transformation about the static axially symmetric self-dual Yang-Mills(SDYM) fields is presented.The theory has proved that the new transformation is a symmetric one.For the two kinds of the Lie algebraic generators of the Lie group SL (N.R)/SO(N),the corresponding transformations are given.By making use of the Yang-Baxter equality and their square brackets we have obtained the Loop and comformal algebraic structures of the symmetric transformations for the basic fields.All the results obtained in this paper can be directly generalized to the other models.     

Nanoscopic surface patterns of diblock copolymer thin films

The surface topography of thin diblock copolymer films is studied by atomic force microscopy (AFM). With AFM an island-to-ribbon transition is observed for symmetric polystyrene-b-poly (4-vinylpyridine) (PS-b-P4VP) on mica with increasing solution concentration. Our study also demonstrates how the formation of the pattern strongly depends on the copolymer composition based on the volume fraction. The substrate and solvent used both have great effects on the morphology of the thin films. Only by using highly polar substrate (mica), can we gain regular pattern. The reason why the regular islands cannot be obtained with symmetric PS-b-P4VP on graphite is also explained. On mica using nonselective and selective solvents, a rather regular pattern can be obtained. The difference is only in the solution concentration for forming regular patterns.     

Symmetries of Euler Equations in Lagrangian Coordinates

Abstract

The transition from Eulerian to Lagrangian coordinates is a nonlocal transformation. In general, isomorphism should not take place between basic Lie groups of studied equations. Besides, in the case of plane and rotational symmetric motion hydrodynamic equations in Lagrangian coordinates are partially integrated. This fact introduces arbitrary functions, initial data, to the resulting systems and makes cuurently central the problem of group classification. It is stated that under a transition to Lagrangian coordinates, the main group becomes infinite–dimensional as well in space coordinates. The exclusive values of arbitrary functions of Lagrange coordinates (vorticity, momentum), at which the further group widening takes place, are found in [1].     

Spherical symmetry of generalized EYMH fields

The possible actions of symmetry groups on generalized Higgs fields coupled to an Einstein–Yang–Mills field are studied with differential geometrical techniques involving principal and associated bundles. A classification of conjugacy classes of these actions and the form of the corresponding invariant Einstein–Yang–Mills–Higgs (EYMH) fields is obtained and then applied to the case of static spherically symmetric fields over four-dimensional space-time. We identify the representations of the gauge group for which spherically symmetric Higgs fields exist. Then the set of all field equations for the independent functions that describe these fields is analyzed and the corresponding ordinary system of differential equations is derived and shown to be consistent.     

The complete system of algebraic invariants for the sixteen-vertex model: I. Derivation via the three-dimensional orthogonal group

In a previous paper, the partition function of the 16-vertex model was shown to be invariant under a group of linear transformations in the space of the vertex weights. According to a theorem by Hilbert, every algebraic invariant such as the partition function for a finite lattice can be expressed algebraically in terms of a finite set of basic algebraic invariants, which are sums of products of the vertex weights. We construct this set by analysing the structural properties of the transformation group (the direct product of two three-dimensional orthogonal groups). The basic set is found to consist of 21 invariants, ranging from a linear invariant up to invariants of the ninth degree. In particular cases, notably the (general or the symmetric) eight-vertex model, the six-vertex model and the free-fermion model, several invariants vanish and a number of additional algebraic relations between the basic invariants are obtained.     

Nonlinear electrodynamics coupled to teleparallel theory of gravity

Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy--momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy--momentum we obtain the value of energy.     

The penrose transform and the topology of certain algebraic varieties

We study the multivaluedness of functions obtained via the Penrose transform. We show that the monodromy group of the Penrose transform of a meromorphic function with an irreducible pole variety is the full symmetric group.Research supported by CNR.     

New Semiclassical and Numerical Approaches to Locate Zeros of Wave Functions Asiri Nanayakkara

A new semiclassical method is presented for evaluating zeros of wave functions. In this method, locating zeros of the wave functions of Schrodinger equation is converted to finding roots of a polynomial. The coefficients of this polynomial are evaluated using WKB and semi quantum action variable methods. For certain potentials WKB expressions for moments are obtained exactly. Almost explicit formulae for moments are obtained for the potential V (x) = xN. Examples are given to illustrate both methods. Using semi quantum action variable method, complex zeros of the wave functions of the PT symmetric complex system V(x) = x4 iAx are obtained. These zeros exhibit complex version of interlacing.     

Cluster states of fermions in the single l-shell model

The paper deals with the ground state structure of the partly filled l-shell of a fermionic gas of atoms of spin s in a spherically symmetric spin independent trap potential. At particle numbers N=n(2s+1), n=1,2,...,2l+1 the basic building blocks are clusters consisting of (2s+1) atoms, whose wave functions are completely symmetric and antisymmetric in space and spin variables, respectively. The creation operator of a cluster is constructed and applied also to create multi cluster states. Ground state energy expressions are derived for the n-cluster states at different l, s values and interpreted in simple terms.