相对运动的动力学方程

引入惯性力广义势的概念，推出非惯性系中的拉格朗日方程，并举例说明了其应用。     

LiSrAlF6晶体Cr3+掺杂中心电子结构的研究

使用离散变分方法(DVM)对LiSrAlF6晶体中以Cr3+为中心的多种分子团簇的电子结构进行了计算.主要研究了镶嵌势、团簇大小、基组类型对单电子能量本征值、基态原子轨道特性的影响,给出了使计算结果趋于收敛的基本条件.     

Dissociation energy of diatomic molecules

The dissociation energy of twelve diatomic molecules has been determined by fitting four-parameter potential functionU(r)=D _e[[1−exp{−b(r−r _e)}]/ [1−Cexp{−b(r−r _e)}]]² to the true Rydberg-Klein-Rees (RKR) curves for their fifteen electronic states using the mean square deviation as the criterion for the selection of the best fit. Average deviation ofD _e has been found to be 2.7% as compared to 20.5% obtained with Lippincott’s potential function for these molecules. In addition the anharmonocity constantω _ex_e has also been calculated for the same electronic states yielding average mean deviation 8.9%.     

圆柱螺旋电磁Wiggler的场形分析

 利用载流圆柱螺旋线系统内部的磁标势满足的Laplace方程, 以及系统磁矢势的积分形式, 定出Laplace方程通解的未知系数, 求得左(右)旋单绕圆柱螺旋线的磁标势。应用磁场的叠加原理以及积分法, 给出了各种类型如双绕、双双绕、交叉绕等螺旋形Wiggler的场形分布公式。     

五种典型硝基苯胺类炸药的静电势与撞击感度的关系研究

利用HONDO程序包,采用从头算法对硝基苯胺类炸药的分子结构和电偶极矩等性质以及 C-NO2键中点静电势等进行计算,讨论了硝基苯胺类炸药C-NO2键中点静电势最大值Vmidmax与其实验撞击感度之间的关系.研究表明:对于硝基苯胺类炸药,不宜单独用C-NO2键中点静电势最大值Vmidmax来表征撞击感度的变化,但可以用静电势最大值Vmidmax与电偶极矩的积来确定其撞击感度的变化趋势,讨论了硝基和胺基的相对位置以及硝基和胺基的数目对这类炸药感度的影响.     

量子阱中的束缚极化子的路径积分变分研究

利用Feynman路径积分变分方法，推导了整个电声子耦合区域的量子阱中束缚极化子的基态能。对其数值结果研究表明：当量子阱的约束势达到一定值，极化子的基态能修正－△E随电声子耦合常数α的增加激剧增大，约束势导致有效电声子耦合从无约束势时的弱耦合向居间耦合或强耦合渡越。更重要的是，我们发现存在一个量子阱的临界有效宽度lz0,当lZ小于临界值时，－△E随lz变小很快增大；当lz大于临界值时，随lz变大，－△E几乎不变。     

用对比法深入认识速度势

介绍了运用对比法深入认识速度势的一种方法,圆满地解决了学生对速度势的深入认识及灵活运用问题.     

几种不同形状导体表面的电荷面密度

对无限大导体表面，楔形导体表面，半圆柱形凸起表面电荷面密度进行了具体的计算，结果表明在静电平衡的条件下导体表面虽曲率相同，但表面电荷面密度却可以不同．     

Spectroscopically determined potential energy surfaces of the H2O, H2O, and H2O isotopologues of water

Adiabatic potential energy surfaces (PESs) for three major isotopologues of water, H₂¹⁶O, H₂¹⁷O, and H₂¹⁸O, are constructed by fitting to observed vibration-rotation energy levels of the system using the nuclear motion program DVR3D employing an exact kinetic energy operator. Extensive tests show that the mass-dependent ab initio surfaces due to Polyansky et al. [O.L. Polyansky, A.G. Császár, S.V. Shirin, N.F. Zobov, P. Barletta, J. Tennyson, D.W. Schwenke, P.J. Knowles, Science 299 (2003) 539-542.] provide an excellent starting point for the fits. The refinements are performed using a mass-independent morphing function, which smoothly distorts the original adiabatic ab initio PESs. The best overall fit is based on 1788 experimental energy levels with the rotational quantum number J = 0, 2, and 5. It reproduces these levels with a standard deviation of 0.079 cm⁻¹ and gives, when explicit allowance is made for nonadiabatic rotational effects, excellent predictions for levels up to J = 40. Theoretical linelists for all three isotopologues of water involved in the PES construction were calculated up to 26 000 cm⁻¹ with energy levels up to J = 10. These linelists should make an excellent starting point for spectroscopic modelling and analysis.     

Constructing frames for finite dimensional Hilbert spaces

In this paper, we use the characterization of frames, introduced in [W. Rolli, A characterization of frames for finite dimensional Hilbert spaces, preprint], to construct frames for finite dimensional Hilbert spaces. Furthermore this approach allows for the construction of frames with prescribed properties.