球形空腔内的粒子对内壁作用力的讨论

指出了一道量子力学习题解答的错误,并给出合理的解答,探讨了处于束缚定态的粒子对空腔内壁的平均作用力.     

势垒贯穿中U_0=E时的透射系数研究——也从一道势垒习题的问题谈起

推导出了势垒贯穿问题中当∪0=E时的透射系数表达式,并利用该公式圆满解释了《大学物理》刊出的一篇题为《从一道习题看量子力学中的势垒》文章中提出的问题.     

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.     

一维定态薛定谔方程的宏观模拟解法

将实验模拟法引入量子力学.设计了一个弦振动系统,这个系统的定态方程与定态薛定谔方程数学形式一样,为定态薛定谔方程的模拟解法提供了理论和实验途径.宏观模拟的结果为理解薛定谔方程提供了宏观类比. 关键词： 薛定谔方程 宏观模拟解法     

势垒贯穿中U0=E时的透射系数研究--也从一道势垒习题的问题谈起

推导出了势垒贯穿问题中当U0=E时的透射系数表达式,并利用该公式圆满解释了《大学物理》刊出的一篇题为《从一道习题看量子力学中的势垒》文章中提出的问题     

对一道静电除尘习题流行解答的商榷

通过分析气体电离导电、金属导电和电解液导电的不同产生机理,对一道常见静电除尘习题,从物理原理及电流定义两方面阐述了与资料上广泛流行解法和答案的不同见解.     

应该公开纠正的一个错误答案

本文指出了一些电动力学教材中一个习题答案的错误，并给出了两种正确解法．导致此错的解法已延续多年，有公开纠正之必要．     

一道典型力学习题的多种解法

本文介绍了一道典型力学习题的多种解法，并对各种解法的求解思路和方法作了简单点评．     

傅里叶变换法求解两类简单的薛定谔方程

自由粒子和一维无限深势阱的薛定谔方程的求解是量子力学较为基础的内容.本文采用傅里叶变换对这两类简单的薛定谔方程进行了求解讨论.通过偏微分方程的傅里叶变换解法和偏微分方程作分离变数成常微分方程后的傅里叶变换解法的深入讨论,均得到与有关教材一致的结果,并讨论了这两种方法之间的差别和联系.     

一个特殊回路上感生电动势的计算

《物理教师》2007年第2期倪志强等老师《探析感应电动势——对一道习题及解法的商榷》一文中,有这样的一个习题： 如图1所示,用均匀导线做成的矩形线框,每边长0．2m,正方形的一半放在垂直纸面向里的匀强磁场中,     

探测二茂铁外价轨道(e,2e)反应中的扭曲波效应

利用第三代高效率电子动量谱仪,分别在600和1500 eV两种不同入射电子能量下获得了二茂铁(ferrocene)分子外价轨道的电离能谱和电子动量谱的相关实验结果.并利用非相对论与标量相对论密度泛函方法计算出了二茂铁的重叠型和交错型两种不同构象的理论动量谱.两种构象的外价轨道一一对应,理论电子动量谱基本一样.对二茂铁的外价轨道,在低动量区观测到了强烈的扭曲波效应,这与这些轨道主要由铁原子的3d轨道构成有关.通过相对论和非相对论计算结果的比较,表明相对论效应对于二茂铁的外轨道动量分布几乎没有影响. 关键词： 二茂铁分子 电子动量谱 相对论效应 扭曲波效应     

On the Coulomb and higher-order sum rules in the relativistic Fermi gas

Two different methods for establishing a space-like Coulomb sum rule for the relativistic Fermi gas are compared. Both of them divide the charge response by a normalizing factor such that the reduced response thus obtained fulfills the sum rule at large momentum transfer. To determine the factor, in the first approach one exploits the scaling property of the longitudinal response function, while in the second one enforces the completeness of the states in the space-like domain via the Foldy-Wouthuysen transformation. The energy-weighted and the squared-energy-weighted sum rules for the reduced responses are explored as well and the extension to momentum distributions that are more general than a step-function is also considered. The two methods yield reduced responses and Coulomb sum rules that saturate in the non-Pauli-blocked region, which can hardly be distinguished for Fermi momenta appropriate to atomic nuclei. Notably the sum rule obtained in the Foldy-Wouthuysen approach coincides with the well-known non-relativistic one. Only at quite large momentum transfers (say 1 GeV/c) does a modest softening of the Foldy-Wouthuysen reduced response with respect to that obtained in the scaling framework show up. The two responses have the same half-width to second order in the Fermi momentum expansion. However, when distributions extending to momenta larger than that at the Fermi surface are employed, then in both methods the Coulomb sum rule saturates only if the normalizing factors are appropriately modified to account for the high momentum components of the nucleons.     

Self Similarity of Cross‐Stream Droplet Momentum Displacement in Dispersed Multiphase Flow

Analytical methods are developed and applied to droplet motion, as it relates to aircraft icing. Impinging droplets largely affect the heat balance at an iced aircraft surface, as well as the final ice shape. In this study, a similarity solution of the Eulerian droplet momentum equation is developed. Droplet motion near a flat plate is investigated with a similarity solution. By using scaling, sensitivity, order of magnitude and similarity methods, a momentum displacement of droplets (or particles) due to the presence of the solid surface is predicted. Self similarity of the droplet profiles is established, such that downstream propagation can be expressed in terms of a single independent coordinate. Limiting trends of momentum/drag induced and Blasius‐diffusion profiles are found to identify the spatial range encompassing the droplet motion. The predicted results are successfully compared against the scaling requirements.     

Quantum mechanics: cleaning up metaphysical baggage

The dynamic electronic structure of atoms and molecules can be directly observed by means of the (e, 2e) reaction, which measures the distribution of energies and momenta of two electrons in coincidence after a knockout reaction initiated by an electron beam of known momentum incident on a molecular gas target. The molecular state for each event is identified by the electron separation energy. The recoil momentum for each event is known from the difference of measured initial and final momenta. It has been verified that values of this momentum are equal under suitable conditions to the momentum of the electron in the target immediately before knockout. Thus the spherically-averaged electron momentum distribution for each molecular orbital is measured. This is directly related to molecular orbitals calculated by the methods of quantum chemistry. Properties obtained by this method for different types of molecules are discussed.     

On the Constraint of Transverse Momentum Conservation to Dynamic Fluctuations in High Energy Collisions

The influence from the transverse momentum conservation of the final particles to the scaling of factorial moments is studied in some detail.The experimental results on the “falling down”of factorial moments in azimuthal angle variable are explained successfully.Two new methods are proposed for calculating the factorial moments in order to eliminate the influence of momentum conservation partly and resume the inherent scaling of the fractal system.     

Electron Momentum Spectroscopy of Ethanethiol Complete Valence Shell

利用(e,2e)电子动量谱学手段首次测量了乙硫醇分子全部价轨道的束缚能谱和电子动量分布. 谱仪采用非共面对称的运动学条件,入射电子能量为1.2 keV加束缚能. 实验结果与密度泛函和Hartree-Fock方法的理论计算结果基本相符. 在束缚能谱中,观察到了17.8 eV的可能的伴线,并用电子动量谱进行了研究和标识.     

Estimated efficiency of the deflection of a dangerous space object using an explosion or impact

The efficiency of various methods for deflection of dangerous space objects (e.g., asteroids) is studied. The main physical processes related to a distant nuclear explosion are analyzed, and a mechanical momentum is calculated. Mechanical momenta resulting from explosions of buried nuclear and chemical charges are quantitatively estimated. Approximate expressions for estimation of the mechanical momentum related to explosion or high-velocity impact are derived. The topicality of the protection of the earth from dangerous space objects and the corresponding particular problems are discussed.     

Longitudinal momentum distributions in stripping reactions with halo nuclei

Differential cross sections and longitudinal momentum distributions of observed particles are calculated for stripping reactions that result from diffractive interaction between halo nuclei and targets. The applicability of different analytic methods of calculation is considered. The advantages of an improved approximation of small target radius are demonstrated for valent halo nucleon absorption radii of 2–4 fm in describing momentum distributions in particular.     

UF_6分子价轨道相对论效应的理论电子动量谱学研究

用非相对论、标量相对论和二分量相对论三种不同的密度泛函方法对UF_6分子的电子结构进行了量子化学计算,并利用编写的程序计算出了三种方法下各个价轨道的电子动量谱,比较了三种方法计算的价轨道能级及动量分布的差异.结果表明,相对论效应不仅使UF_6的能级劈裂和移动,而且对部分价轨道电子动量分布有显著的影响.     

Optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian–Eulerian methods

A new optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian–Eulerian hydro methods is described. Fluxes of conserved variables – mass and momentum – are limited in a synchronous way to preserve local bounds of primitive variables – density and velocity.