关于三维各向同性谐振子径向矩阵元计算的讨论

根据广义Laguerre多项式的数学性质，导出了较为简单的三维各向同性谐振子径向矩阵元的普遍公式,并在这基础上计算了一些重要特殊情形的径向矩阵元: 矢径r整数次幂的平均值，电偶极跃迁矩阵元和电四极跃迁矩阵元. 关键词： 三维各向同性谐振子 径向矩阵元 广义Laguerre多项式 偶极跃迁 四极跃迁     

环形振子径向矩阵元的通项表达式及其递推关系

利用文献1给出的环形振子的归一化的径向波函数,推导出环形振子径向矩阵元的通项表达式及其递推关系.解决了环形振子径向矩阵元的计算问题.     

新环形库仑势的束缚连续跃迁矩阵元

利用新环形库仑势的归一化的束缚态径向波函数和按“k/2π标度”归一化的散射态径向波函数,本文给出了新环形库仑势的任意幂次的束缚连续跃迁矩阵元的通项表达式.为了简化高幂次的束缚连续跃迁矩阵元的计算,我们还推导出了不同幂次的束缚连续跃迁矩阵元之间所满足的递推关系,并提出了计算径向波函数微商的矩阵元的计算办法.本文结果可广泛的用于原子与分子的散射问题特别是环形分子的散射问题之中.     

船舰尾流前向散射的缪勒矩阵特性研究

从米氏散射理论出发,利用单次散射理论模型研究了船舰尾流前向散射缪勒矩阵(FSMMBSW)的分布模式,以及矩阵元与气泡数密度、气泡半径之间的关系.研究表明,气泡米氏散射缪勒矩阵元m2和m4在前向90°存在较大振荡,且振荡幅度随半径增大而增大;气泡幕前向散射缪勒矩阵元M11和M44无方位变化,有方位变化的矩阵元随方位角正弦...     

华德等式和贝特-沙尔披特方程、介子和重子的电磁跃迁矩阵元

在这篇文章中,用华德等式给出了介子、重子的贝特-沙尔披特方程的积分核与其电流跃迁矩阵元的积分核的关系,用这些关系作为讨论方程和跃迁矩阵元时做的假定的限制,从而使电流守恒得到保证.文中在不考虑封闭的层子线圈图的贡献时,用华德等式给出的关系可从贝特-沙尔披特方程的积分核将电流跃迁矩阵元的积分核算出来.文中在对方程的积分核作位势假定以后,得到了跃迁矩阵元的表达式.用方程的核和解出的波函数可将电流跃迁矩阵元算出,而且保证电流守恒.     

光偏振态的群论描述:转动矩阵的生成元

应用偏振光描述中的变换矩阵与群论的对应关系[1]和相应的计算理论,讨论了与偏振光学系统中的Jones矩阵、Mueller矩阵相对应的SU(2)群、SO(3)群和Lorentz群的生成元问题,给出了用单位矩阵、Pauli自旋矩阵和稀疏矩阵分别作为无耗偏振光学系统中SU(2)群元(Jones矩阵)和SO(3)群元(Mueller矩阵)生成元以及部分损耗偏振光学系统中的幺模群(Jones矩阵)和Lorentz群(Mueller矩阵)生成元的具体形式;矩阵计算理论说明这些群元的生成元表示可以简化偏振光学系统的计算。     

Zn Belavin模型的反射矩阵

本文得到了Zⁿ Belavin模型反射矩阵的矩阵元表达式,在退化到三角极限后,得到了非对角的三角统计模型的反射矩阵.     

多维耦合受迫量子谐振子的普遍解

运用广义线性量子变换的普遍理论求解多维耦合受迫量子谐振子，给出了系统演化算符的矩阵元、波函数、力学量期望值和配分函数的严格表达式. 关键词： 多维耦合受迫量子谐振子 演化算符矩阵元 配分函数     

偏振光大气传输的前向散射新模型

建立了偏振光空间传输前向散射的物理模型。对各向同性散射介质,在非相干性假设条件下,导出了偏振光双散射和多散射前向散射的有效Mueller矩阵,给出了偏振光Mie散射前向有效Mueller矩阵各矩阵元之间的对称性关系,即Mueller矩阵的16个矩阵元中只有7个是独立的,其他9个矩阵元通过组合及一定角度的旋转即可得到。利用Monte Carol方法模拟了偏振光在空间传输10km的前向散射的有效Mueller矩阵,模拟结果表明各矩阵元存在一定的对称性关系,与基于本模型导出的偏振光前向散射的有效Mueller矩阵元具有较好的一致性。     

N维各向同性谐振子径向矩阵元的递推公式

各向同性谐振子是量子理论中能够严格求解的可解势场之一.对它的研究和讨论,在理论上和实际的应用中都有重要意义.本文推导出了N维(N≥2)各向同性谐振子径向矩阵元〈nrl|rk|nr′l′〉的递推公式,在此基础上得到了平均值的递推公式,并且讨论了维各向同性谐振子径向矩阵元的递推公式的一般性,而文献[3]与[4]所给出的各向同性谐振子径向矩阵元的递推公式只是本文结论的特例.     

Fluorescence in a Quantum System with Violated Symmetry

The model of a single multilevel one-electron atom with violated symmetry such that its transition dipole-moment operator has constant diagonal matrix elements, among which not all are pairwise equal to each other, has been studied. It has been shown that the expression for the far electromagnetic field of such an atom does not contain any appreciable contributions from the diagonal matrix elements of the transition dipole moment in an explicit form; thus, these matrix elements have an effect on fluorescence via the time dependence of non-diagonal matrix elements due to quantum non-linear processes of higher orders. It has also been demonstrated that a two-level quantum system, whose transition dipole operator has constant unequal diagonal matrix elements, can continuously fluoresce under excitation with monochromatic laser radiation at a much lower frequency than the frequency of the exciting radiation. The possibility of the experimental detection and practical application of this effect are discussed.     

Analytical Solution of Partial-Wave Faddeev Equations with Application to Scattering and Statistical Mechanical Properties

In this work, the Faddeev equations for three-body scattering at arbitrary angular momentum are exactly solved and the transition matrices for some transition processes, including scattering and rearrangement channels are formulated in terms of free-particle resolvent matrix. A generalized Yamaguchi rank-two nonlocal separable potential has been used to obtain the analytical expressions for partial wave scattering properties of a three-particle system. The partial-wave analysis for some transition processes in a three-particle system is suggested. The partial-wave three-particle transition matrix elements have been constructed via knowledge of the matrix elements of the free motion resolvent.The calculation of a number of scattering properties of interest of the system such as transition matrix and its poles(bound states and resonances) and consequently other related quantities like scattering amplitudes, scattering length,phase shifts and cross sections are feasible in a straightforward manner. Moreover, we obtain a new analytical expression for the third virial coefficient in terms of three-body transition matrix.     

锗硅合金半导体中无声子参与光跃迁机制研究

研究了Ｓｉ１－ｘＧｅｘ合金半导体中无声子参与光嗅迁的产机制，对由杂质无规分布引起的无声子参与光跃迁给出了一个物理模型。用此模型计算了光跃迁偶极矩，给出了跃迁偶极矩的上限。提出了未掺杂Ｓｉ１－ｘＧｅｘ合金半导体中无声子参与光跃迁的一种跃迁机制，认为是Ｇｅ原子周围波函数畸变的集体行为。     

The dependence of the photodisintegration cross section on the off-shell T-matrix

Nucleon-nucleon scattering phase shifts determine the diagonal element of the transition matrix. The off-diagonal elements are not completely arbitrary but have conditions imposed on them by the range and the tail of the potential. Electromagnetic interaction can also be used to place restrictions on the off-diagonal elements. We find that the cross section of the deuteron photodisintegration is sensitive to the off-shell transition matrix. The integrated cross section can be varied by as much as 30 % or more, and the matrix element for the El transition by a factor of 2. While the matrix element for the photodisintegration depends on the off-shell elements of the T-matrix, it cannot be used to discriminate between alternative off-shell T-matrices. We have constructed classes of different off-shell T-matrices, which produce identical photo-disintegration cross sections and other two-body scattering and bound-state properties.     

Quantum-electrodynamic modification of atomic dipole matrix element in a strong converging laser field

In this paper we report at the first time a quantum-electrodynamic modificationresult to the dipole transition matrix elements related to the bound levels of an atom in a strongconverging laser field.When the laser intensity increases,the dipole matrix elements increaseat first.However,further intensity increase will bring about the matrix elements decrease.That means the dipole transition probability is suppressed.     

Derivation of extended boundary condition method from general definition of -matrix elements and Lippman–Schwinger equation for transition operator

Waterman's surface-integral expressions for the T-matrix elements are derived on the basis of the quantum-mechanical potential scattering approach in electromagnetic scattering problem. We use general definition of the elements of the T-matrix as the matrix elements of the dyadic transition operator and Lippman–Schwinger volume integral equation for the dyadic transition operator. The interrelations of the Q- and Waterman's T-matrix with the transition operator are shown.     

Effects of mode-mixing and non-Condon interaction in the vibronic spectra of multimode systems

A method of calculation of optical spectra, which allows one to take into account the mixing of an arbitrary number of modes in the transition, is developed. Thus the dependence of electronic transition matrix elements on nuclear coordinates is also taken into consideration. In this method, the calculation of the Fourier transform of the spectrum is reduced to the calculation of the determinant of the 2N×2N matrix and its reciprocal matrix; the elements of the matrix are given by time-dependent pair-correlation functions.     

锗硅量子阱中近带边光跃迁的理论和实验研究

本文研究了SiGe/Si量子阱中近带边光跃迁的产生机制,对由杂质无规分布引起的近带边光跃迁给出了一个物理模型。用此模型计算了光跃迁偶极矩,给出了跃迁偶极矩的上限。提出了未掺杂SiGe/Si量子阱中近带边光跃迁的一种跃迁机制,认为是Ge原子周围波函数畸变的集体行为。用MBE方法生长了掺杂SiGe/Si量子阱材料,在低温下观测到近带边光跃迁。     

氢原子(e,2e)反应离化振幅的分析

利用双势公式的后滞形式并且在入射的快电子近似的取为平面波的基础上,在共面非对称几何条件下计算了电子离化氢原子的三重微分散射截面.变换矩阵元可以解析的表示为结构散射因子和关联因子的乘积形式(关联因子和结构散射因子分别对应于recoil peak和binary peak)解决了由于大量的数值计算而带来的麻烦.本文引入一个有效电荷,通过对它进行调整考虑了变换矩阵元中的第一项的影响.最后把计算结果与实验结果及他人的结果进行了比较,与实验结果符合的很好.     

The relationship between formal scattering theory and the density matrix

A study has been carried out on the relationship between formal scattering theory and the density matrix formalism. The density operator is developed in terms of the scattering operator S and the observable square modulus matrix elements of S are shown to be equivalent to elements of the density matrix. The Møller wave operators are similarly treated and subsequently used in obtaining the density matrix expression for the transition matrix. Finally, using the latter, it is shown that the hierarchy of approximations to the density matrix yields equivalent results to those obtained from the Born series.