多原子分子高激发振动能谱的非线性量子理论计算的程序化

以占有数表象为基础,通过编程,实现了不同分子各激发态波函数的基、基矢、完备的基矢空间及该空间中的Ｈａｍｉｕｌｔｏｎｉａｎ算符距阵元的计算,在此基础上实现了多原子分子高激发振动的能谱的非一量子理论计算的程序化。     

《量子力学》自学辅导之七—表象理论（续）

《量子力学》自学辅导之七──表象理论（续）曾心愉，宋宇辰，斐文杰（复旦大学物理系，复旦大学理论物理骨干教师班，上海２００４３３）４量子力学公式的矩阵表述（分立谱为例）实质上是把ｘ表象中的达式变换到Ｑ表象中，故以Ｑ表象基矢ｕ（ｘ）为基础，以态矢及算符（...     

Murrell-Sorbie势分子体系振-转能级结构

对双原子分子体系内部相互作用势作了物理分析与比较,引用Murrell-Sorbie势.然后应用泰勒微扰理论.将M-S势函数泰勒展开,并取至4次方项,建立了相应的定态薛定谔方程.然后用三维谐振子势能量表象的径向矩阵对角元的简要形式,简易有效地求得一级微扰能量,进而获得双原子分子体系振-转能级的解析形式.其某些低能级和光谱的理论值与实验结果相符.     

离子键分子振-转能级与光谱

对离子键分子内部势能函数进行了几何与物理分析,全面分析了4种分子键的贡献,克服了仅考虑马德隆势的不足,引入极化势与范德华势,建立了较全面精准适用的离子相互作用能量函数.求解了相应薛定谔方程,并引入了马德隆势的能量表象的Kramer公式,导出了能级的解析解.对氯化钠分子基态能量和基跃迁频率作了计算,其结果与实验值很好的符合.量子力学,量子理论是本科教学重要基础,本文在加深微扰论、表象理论、算符矩阵运算和矩阵元计算等内容的理解与应用是具体生动的,对本科生今后从事教学(大学)和升入更深层次的学习是很重要的.     

在局域子空间中计算给定范围内的能量本征值

通过能量算符δ函数作用于完全随机格点波函数,构造了可用于直接计算给定范围[Emin,Emax]内能量本征值和本征函数的局域子空间.在非正交局域基下详细推导了交迭积分和哈密顿算符在分立位置表象中的表示,讨论了广义本征值问题的解法.以Morse势和Henon-Heiles势的多个能量范围为例检验了算法     

乙烯和乙炔基在Ni(110)表面上吸附结构的研究

采用平面波赝势方法，利用基于从头计算的软件包，对乙烯和乙炔基在Ni(110)表面上吸附的问题进行了计算. 在低覆盖度时，孤立的乙烯分子的吸附能比密集时高，乙烯分子的C-C 轴大致沿衬底的Ni原子链方向(即沿［110］晶向)，C-C轴与衬底Ni(110)表面有12°的倾斜角，乙烯分子的C—C键的键长为 0.147nm. 乙烯分子中接近顶位的C原子与衬底中距离最近的Ni原子为0.199nm. 在高覆盖度时，乙烯分子在Ni(110)表面上形成c(2×4)再构，每个表面二维元胞中有两个乙烯分子，每个乙烯分子的吸附位置与低覆盖度时相似，而C—C键长比低覆盖度时要短. 乙炔基是乙烯在Ni(110)表面上分解的产物. 关于乙炔基的计算结果表明：乙炔基的两个C原子的间距为0.131nm，比乙烯分子中C原子的间距更短. 与乙烯分子相比，乙炔基的吸附位置更靠近顶位. H原子与吸附在顶位上的C原子相连接，C—H键也大致沿衬底的Ni原子链方向，与Ni表面呈45°的倾斜角. 关键词： 乙烯和乙炔基 平面波赝势方法 吸附几何结构     

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…     

四参数双原子分子势阱中相对论粒子的束缚态

给出了具有四参数双原子分子势型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： 四参数双原子分子势 Klein-Gordon方程 Dirac方程 束缚态     

微扰论计算Morse势的能级

用微扰论计算出双原子分子Morse势的能级,并与光谱中双原子分子的能级的经验公式比较,十分吻合。     

Be-CO(X1∑+)体系的冷碰撞动力学

基于碱土金属原子Be和分子CO精确的相互作用势，采用对数-导数传播子方法和非耦合角动量表象，计算低和超低能碰撞条件下Be-CO体系在电场中的碰撞动力学，获得若干电场中碰撞体系低场追索态的弹性和非弹性碰撞截面，预测Be原子感应冷却CO分子的可行性.     

Recommendations for enhancing the role of the auditory modality for processing sonar data

Submarine warfare continues to pose a threat in present-day military operations. Visual displays play a dominant role for operator detection and classification of underwater and surface targets. However, the visual modality is ineffective for the detection of transient signals. In spite of quieter submarines, transient sounds such as hull popping are difficult to disguise, which makes them more likely to be detected via an auditory display. Operators tend to use auditory displays less often because several factors can impede effective aural processing. In this paper, the sonar problem is reviewed followed by some proposed techniques for making more effective use of the auditory modality for the presentation of sonar signals as a means of further improving operator detection and classification of targets. Some recommendations for augmenting the aural presentation of sonar signals over headphones are then discussed. Key research areas include: (1) a reduction of the sound level of the ambient noise in noisy environments should improve the likelihood that the operator will detect weak signals; (2) the provision to replay sound bites of interest and to compare these against a library of known archetypes should lead to increased accuracy in target classification; (3) the ability to present sonar beams in a three-dimensional auditory display where the spatial position of each sonar beam corresponds to the actual position of the source in the ocean should enable the operator to monitor multiple beams and increase his/her situational awareness. Ultimately, the viability of an auditory display is dependent on operator hearing acuity.     

基于图像边缘能量的自动聚焦算法

聚焦过程中,不同离焦点其图像差异体现在高频能量上。利用Sobel算子边缘检测算法,提出了图像边缘能量清晰度评价函数。与方差法和梯度能量法相比,该评价函数具有更好的尖锐性,能够适应高精度聚焦的需要。通过改进爬山算法,充分利用爬山过程中的先验知识,提出了随机起点爬山算法。该算法能够减少爬山步数,可提高自动聚焦速度。     

Comparison of a subrank to a full-rank time-reversal operator in a dynamic ocean

This paper investigates the application of time-reversal techniques to the detection and ensonification of a target of interest. The focusing method is based on a generalization of time-reversal operator techniques. A subrank time-reversal operator is derived and implemented using a discrete set of transmission beams to ensonify a region of interest. In a dynamic ocean simulation, target focusing using a subrank matrix is shown to be superior to using a full-rank matrix, specifically when the subrank matrix is captured in a period shorter than the coherence time of the modeled environment. Backscatter from the point target was propagated to a vertical 64-element source-receiver array and processed to form the sub-rank time-reversal operator matrix. The eigenvector corresponding to the strongest eigenvalue of the time-reversal operator was shown to focus energy on the target in simulation. Modeled results will be augmented by a limited at-sea experiment conducted on the New Jersey shelf in April-May 2004 measured low-frequency backscattered signal from an artificial target (echo repeater).     

An exact energy conservation property of the quantum lattice Boltzmann algorithm

The quantum lattice Boltzmann algorithm offers a unitary and readily parallelisable discretisation of the Dirac equation that is free of the fermion-doubling problem. The expectation of the discrete time-advance operator is an exact invariant of the algorithm. Its imaginary part determines the expectation of the Hamiltonian operator, the energy of the solution, with an accuracy that is consistent with the overall accuracy of the algorithm. In the one-dimensional case, this accuracy may be increased from first to second order using a variable transformation. The three-dimensional quantum lattice Boltzmann algorithm uses operator splitting to approximate evolution under the three-dimensional Dirac equation by a sequence of solutions of one-dimensional Dirac equations. The three-dimensional algorithm thus inherits the energy conservation property of the one-dimensional algorithm, although the implementation shown remains only first-order accurate due to the splitting error.     

A new model for ideal gases. Decay to the Maxwellian distribution

In this work, a new model in kinetic gas theory for deriving the Maxwellian velocity distribution (MVD) is proposed. We construct an operator that governs the discrete time evolution of the velocity distribution. This operator, which conserves the momentum and the energy of the ideal gas, has the MVD as a fixed point. Moreover, for any initial out-of-equilibrium velocity distribution, it is shown that the gas decays to the equilibrium distribution, that is, to the MVD.     

阶梯算符本征态下介观电子谐振腔的量子效应

基于电荷取分立值的事实,运用阶梯算符的性质,计算电荷、电流以及能量的量子涨落,研究介观电子谐振腔的量子效应.结果表明,计及电荷量子化的事实,在阶梯算符本征态下介观电子谐振腔中电流的量子涨落为零,而电荷与能量的量子涨落不为零,分别与电荷的量子化性质有关,大小决定于系统自感、电容、栅压和形状因子以及状态参量等因素.     

Exact expression for the projected energy

The angle integrated exact expression for the projected energy is derived from two different expansions of the rotation operator. In one, the spin matrix polynomial expansion method is used while in the other the disentangling theorem for angular momentum operator is used.     

Vibrational resonances of non-rotating HCN in the excited electronic state

A multi reference internally contracted configuration interaction (MRCI) method is used to generate the potential energy function (PEF) of the excited electronic state of HCN molecule. The analytic representation of the PEF is employed to calculate complex eigenvalues (resonance positions and widths) by a discrete variable representation (DVR) of the Hamiltonian for the non-rotating (J =0) molecule. The computational method used is a variant of the filter-diagonalization technique based on a recursive polynomial expansion of the absorbing-boundary-conditions (ABC) Green operator. Reasonable agreement with existing experimental data is found. Received 27 July 1999 and Received in final form 18 October 1999