电场中氢原子的概率密度分布与电偶极矩

通过数值计算方法分析了斯塔克效应中氢原子电子的概率密度分布图像,讨论了电偶极矩的指向与概率密度图像之间的关系.     

氢原子电子云的计算和可视化分析

介绍了氢原子中"电子云"的计算机基本作图方法,一种是蒙特卡罗法,另一种是逐点扫描法.利用MATLAB软件.从不同角度对氢原子各种状态下的电子云三维立体分布进行了可视化,使氢原子中电子概率密度的教学更加直观.     

居民出行分布中的电子云现象

研究发现，居民出行分布的概率密度曲线与氢原子基态电子在核外出现的概率密度曲线极为相似，运用量子力学中的电子云分布模型可以很好地解释居民出行分布特性，根据氢原子中电子的径向概率密度函数建立了模拟电子云居民出行分布模型.利用长春市和旧金山地区的抽样调查数据对模型进行了验证.在此基础上，进一步建立了实用模型，并结合实例给出了模型标定方法和过程.该模型可在城市规划和城市交通规划中定量描述居民出行分布状态. 关键词： 科学与社会 自组织系统 电子云 出行分布     

氢原子电子云密度分布分析

通过数值计算形象地分析了氢原子中电子概率密度的分布情况,对此做了一些有别于传统认识的讨论,并由此引出了对粒子运动和波函数概率解释的认识。     

MATLAB在量子力学学习中的应用

指出了《工科量子力学学习中的常用数学工具》一文中的一些差错,列出了正确的公式.量子力学的公式比较多,解决计算问题的最佳工具应该是MATLAB.用MATLAB说明了极限的算法,积分的算法,常微分方程的解法,狄拉克函数的表示和算法,伽玛函数和贝塔函数的用法,特殊函数的算法.以一维线性谐振子为例,说明了MATLAB在量子力学中的应用.MATLAB还能计算氢原子中电子出现的概率密度,并用图形表现出来.     

氢原子电子云的蒙特卡罗模拟

根据量子力学原理,氢原子中电子的几率分布由电子的定态波函数可以唯一地确定.在大多数教科书中,通常是将电子沿径向和角度方向的几率分布分别进行讨论,因此很难给出电子在整个空间几率分布的一个完整图象.我们使用蒙特卡罗随机抽样的方法,通过计算机作图形象而逼真地绘制了氢原子中电子的几率分布图,即所谓的电子云.下面介绍所使用的方法.     

3d电子在立方晶场中的能级和波函数及概率密度图

应用简并微扰论计算了一个3d态的氢原子处于立方晶场中的能级和波函数,并用数学软件Matlab精确地图示了3d电子在立方晶场中的概率密度．     

基于MATLAB氢原子本征函数的关系图示

应用MATLAB的程序绘制氢原子本征态径向波函数、径向密度函数和径向分布函数与矢径的关系图示、s、P、d等电子角分布函数的图示。     

栅氧化层经时击穿的非平衡统计理论分析方法

栅氧化层的经时击穿作为影响互补型金属-氧化物-半导体集成电路可靠性的一个重要因素,一直是国内外学者研究的重点.为了对其进一步研究,首先从栅氧化层在电应力下经时击穿的微观机理出发,基于栅氧化层中电子陷阱密度累积达到临界值时发生击穿的原理和电子陷阱生成过程的随机性,提出了栅氧化层经时击穿的非平衡统计理论分析方法,然后分别给出了恒定电流应力和恒定电压应力下电子陷阱生成速率方程,导出了电子陷阱密度的概率密度分布函数.最后以具体器件为例进行分析,得到了栅氧化层的最概然寿命随电流应力、电压应力及其厚度的变化规律,并类比固体断裂现象中"疲劳极限"的概念定义"击穿极限"概念.计算出了累积失效率随电流应力、电压应力和时间的变化规律,引入特征值来描述累积失效率达到0.63所用的时间.结果表明:电子陷阱密度的概率密度分布函数满足对数正态分布,且理论结果与实验结果相符.     

利用一维Vlasov和Maxwell方程模拟激光等离子体相互作用

应用一维Vlasov和Maxwell耦合程序详细研究了激光等离子体相互作用中的基本问题——受激拉曼散射(SRS). 通过研究发现, SRS的产生与电子速度分布函数在相空间中的结构密切相关, 当电子速度分布函数形成相空间涡旋时,背向SRS光大幅增加,而当电子等离子体波相速度附近的电子速度分布函数曲线变平坦后, 背向SRS光基本停止发生. 在模拟中观测到了SRS的爆发、电子速度分布函数形成相空间涡旋、电子俘获等清晰的物理图像. 关键词： Vlasov-Maxwell模拟 受激拉曼散射     

Photoionization microscopy of Rydberg hydrogen atom near a dielectric surface

Based on the semiclassical analysis of photoionization microscopy, we study the ionization of the Rydberg hydrogen atom near a dielectric surface. The radial electron probability density distributions on a given detector plane are calculated at different scaled energies and near different dielectric surfaces. We find due to the interference effect of different types of electron trajectories arriving at a given point on the detector plane, oscillatory structures appear in the electron probability density distributions. With the increase in the scaled energy, more types of electron ionization trajectories appear and the oscillatory structure in the electron probability density distributions becomes complex. Besides, the dielectric constant of the dielectric surface can also affect the electron probability density distributions. Since the photoionization microscopy interference pattern recorded on the detector plane reflects the distribution of the square modulus of the transverse component of the electronic wave function, with the recorded interference pattern, we can investigate the ionization dynamics of the Rydberg atom near surfaces clearly. This study provides some reference values for the future experiment research on the photoionization microscopy of the Rydberg atom near dielectric surfaces.     

氢原子波函数的经典极限分析

由电子绕原子核的经典轨道运动出发,对电子的椭圆轨道初始坐标参数求平均,得到空间密度分布。这分布与经典极限条件下氢原子中定态几率密度相同。类似的比较也推广到相空间进行。由这一比较得出结论:定态氢原子波函数不描述单个原子而描述一个系综。 关键词：     

氢原子电子云空间分布的可视化

利用Matlab实现了氢原子电子云空间分布的可视化,输入任一组满足取值条件的量子数n、l、m,可同时给出该状态下氢原子径向几率密度曲线、角向几率密度曲线、三维空间几率分布以及三维空间等几率面,便于多视角地理解氢原子电子云的空间分布．     

Recombination of hydrogen atoms on fine-grain graphite

The probability of recombination of hydrogen atoms on surfaces of fine-grain graphite EK98 was investigated as a function of surface roughness. The source of hydrogen atoms used in this experiment was weakly ionised plasma created with an inductively coupled radiofrequency generator at pressures from 30 Pa to 175 Pa in hydrogen. Hydrogen atom density was measured by means of fibre optic catalytic probes. The recombination coefficient of the graphite samples was determined by observing their impact on the spatial distribution of the atom density in a closed side-arm of the reactor. Smith's diffusion model was used to calculate the values of the recombination coefficient. The measured recombination coefficient was found to increase much faster than the measured effective surface. This discrepancy is explained by the fact that on a surface which is not perfectly flat, there is a finite probability for multiple collisions. Impinging atoms collide more than once with the surface before they are reflected into the surface, which results in a larger probability of recombination.     

Theoretical study of the migration of the hydrogen atom adsorbed on aluminum nanowire

We study the behavior of a hydrogen atom adsorbed on aluminum nanowire based on density functional theory. In this study, we focus on the electronic structure, potential energy surface (PES), and quantum mechanical effects on hydrogen and deuterium atoms. The activation energy of the diffusion of a hydrogen atom to the axis direction is derived as 0.19 eV from PES calculations. The probability density, which is calculated by including quantum effects, is localized on an aluminum top site in both cases of hydrogen and deuterium atoms of the ground state. In addition, some excited states are distributed between aluminum atoms on the surface of the nanowire. The energy difference between the ground state and these excited states are below 0.1 eV, which is much smaller than the activation energy of PES calculations. Thus using these excited states, hydrogen and deuterium atoms may move to the axial direction easily. We also discuss the electronic structure of the nanowire surface using quantum energy density defined by one of the authors.     

二维氢原子中的基态奇异特性数值精确对角化法

利用数值有限差分法处理二维氢原子的基态波函数时,计算结果发现其存在着数值奇异特性.本文通过构造一套具有正交完备性的离散贝塞尔基函数,并结合基于Lanczos技术的数值精确对角化方法研究二维氢原子中的基态波函数的数值奇异特性,得到的波函数数值解及其相应的本征能量均与解析结果相一致.这套新的完备的离散贝塞尔基函数,可以在研究一些波函数具有数值奇异特性的体系中发挥至关重要的作用.     

富勒稀C36的电子结构与电子传导

本文采用基于第一性原理的密度泛函理论和非平衡格林函数方法研究了C36分子的电子结构和电子传导特性．本文以Au(1,1,1)为电极分别建立了4个电子输运模型,分别计算了他们的电子传输概率、伏安曲线,同时分析了产生这些分子器件电子输运性质的原因．研究计算结果发现, C36的电子输运主要发生在分子壳上,当左、右电极分别连接在第6号和第35号碳原子两端时,C36的电子输运性能最好,伏安曲线显示该分子具有半导体特性．     

Grassmann phase space methods for fermions. I. Mode theory

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggest the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum–atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics.