在普通物理教学中应用初等数学推导物理公式

在现行的普通物理学及医学院校等所专用的物理学教材中,许多物理公式的推导,大都采用高等数学,而对于物理意义的阐述则是比较简略的。某些院校开设普通物理作为必修课时,并没有设置高等数学课,即或开设高等数学课,不少内容也常是在学生学习积分学之前讲授的,因而课堂讲授往往不能应用高等数学推导某些物理公式。而自学普通物理者,因缺乏高等数学知识,也不能很好地了解某些物理公     

高等数学解决物理问题的三步教学法

针对大学一、二年级的非物理专业学生不习惯、不善于运用高等数学处理随时间或空间变化的物理问题，我们采用三步教学法进行讲解训练，使学生逐步掌握了用高等数学解决物理问题的方法，对学生以后运用高等数学解决专业问题可以起到引导和示范的作用。     

黑体辐射的Mathematica物理实验

＂数学实验＂被公认为是提高高等数学教育水平的有效手段.受此启发,笔者尝试着为高年级工科学生开设了十几项Mathematica物理实验.量子力学、统计物理、固体物理中诸多内容,     

采用一维无穷电阻网络的物理模型求解Fejer积分

高等数学和大学物理是高校理工类学生非常重要的公共基础课.在传统教学中高等数学通常作为工具来帮助解决大学物理问题,而运用大学物理学知识去解决高等数学问题却很少关注.探讨如何把两者的教学结合起来,对培养学生创新思维具有十分重要的意义.本文基于一维无穷电阻网的物理模型,推导出了一维无穷电阻网络等效电阻的解析解,并给出了求解Fejer积分的一种新的物理方法,体现了数理结合的思想.     

在普通物理教学中应用初等数学推导物理公式

在现行的普通物理学及医学院校等所专用的物理学教材中,许多物理公式的推导,大都采用高等数学,而对于物理意义的阐述则是比较简略的。某些院校开设普通物理作为必修课时,并没有设置高等数学课,郎或开设高等数学课,不少内容也常是在学生学习积分学之前讲授的,因而课堂讲授往往不能应用高等数学推导某些物理公式。而自学普通物理者,因缺乏高等数学知识,也不能很好地了解某些物理公式的由来。在讲授物理时,对于物理公式完全不加推导,将会导致学生盲目死背公式或者生硬的搬用公式。学生在学习物理学的过程中,也常迫问公式的来源,以要求对公式有较彻底     

数学工具与物理知识有效结合的探讨——以《大学物理学》课程教学为例

《大学物理学》与高中阶段物理学教材的一个显著区别在于高等数学这一工具的引入,正是基于这一重要的数学工具,学生对有关物理概念的理解以及对具体物理问题的解决都提高到了一个全新的高度。但将本身就具有一定的抽象性和复杂性的数学工具直接用来处理物理问题,大部分学生会感觉难以把握。通过总结教学工作中发现的问题以及积累的经验,分析了如何通过建立一种化抽象为形象的有效机制,将高等数学工具与物理知识恰当结合,从而达到提高教学质量的目标。     

新高考制度下独立院校医学专业医学物理学教学探索

新高考制度下,不同地区学生物理基础差异大,这对高校相关专业,尤其独立院校医学专业物理课教学提出了新的要求.教学实施过程中,突出课堂思政,注重培养品学兼优、对国家有用的人才;注重与中学物理、高等数学的衔接;突出案例教学;与医学知识、物理学史相结合.     

论质点运动学的内禀方程及其应用

在理工科大学物理课程的教学中,一般只讨论变速圆周运动,本文着重讨论自然坐标系及其给出的内禀方程,并举例详述它在求解质点曲线运动问题时的重要性.这对刚学过的高等数学知识可获得一次应用的机会,有助于学生今后对本课程和后续课程的巩固和提高运用高等数学知识解决问题的能力.这也是本课程的＂教学基本要求＂对力学部分施教过程中的一项重要意图.     

大学物理和中学物理教学内容衔接的探讨——以静电场为例

文章以大学物理电磁学静电场部分的教学内容为例,通过对大学和高中物理教学内容的分析,认为:从绪论课开始就要注重把握与高中物理的延续和差异;物理概念的讲授兼顾突破中学物理的思维定势和体现大学物理内在的知识结构和物理思想;物理定理定律的阐释避免机械式的重复,着力解决数学表达式的差异和联系;关注初等数学和高等数学的联系,重视数学表达式的物理内涵等,文章同时给出了加强大学物理和中学物理衔接的建议.     

推荐新书《数学物理方法(修订版)》

<正>数学物理方法课程是高等学校物理类专业学生的必修课之一,该课程以高等数学、普通物理学为基础,又是学习理论物理等后继课程的基础,在物理专业课程中,起着承上启下的重要作用.然而,由于数学工具本身的难度,以及将具体物理问题抽象成数学模型的思想和方法不易掌握,很多学生都对该课程望而生畏.因此,我们特地邀请了北京大学的吴崇试教授,将其从事数学物理方法课程教学四十余年的经验和心得汇集成     

Zitterbewegung of a Model Universe

We investigate the quantum evolution of the metric operators for Bianchi-Type I model universes in the Heisenberg picture in order to remove the need to consider the wave function of the universe and interpret its “spin” variables. The calculation is analogous to that of the Zitterbewegung of the Dirac electron. We consider the behavior of the metric near the classical singularity, and consider the curvature there. Although factor ordering questions preclude the presentation of an unambiguous result for the curvature invariants, it does seem that the classical t ⁻⁴ divergence of the Kretschmann scalar is not removed by quantization.     

Model of a polaron superconductor

This paper studies the mechanism of superconductivity in the case where the electrons are strongly coupled to lattice vibrations and, therefore, are in the state of small polarons. The consideration is based on the Holstein model with zero lattice-vibration dispersion and represents a consistent realization of the BCS approach (with no need arising for boson introduction). The ground state and the excitation spectrum are found. The current states are studied and the criterion of their stability is formulated. The superconducting transition temperature is shown to increase without limit with increasing electron-phonon coupling constant. This is accompanied by an exponential decrease in the critical current. Some fundamental properties of high-temperature superconductors are shown to follow directly from this model.     

Percolation in a Voronoi Competition-Growth Model

We study a model in which two entities (e.g., plant species, political ideas,...) compete for space on a plane, starting from randomly distributed seeds and growing deterministically at possibly different rates. An entity which forms an infinite cluster is considered to dominate over the other (which then cannot percolate). We analyze the occurrence of such a form of domination in situations in which one entity starts from a much larger density of seeds than the other one, but the latter one grows at a much faster rate than the former one. The model studied here generalizes the problem of Voronoi percolation.     

Proton-Proton Interaction in a Dual Model

The “background-pomeron” component of the amplitude is studied in the framework of a dual model with square-root trajectories. Double pomeron poles are used as vacuum exchanges in various channels, with exotic Regge poles dual to them. The expressions obtained are applied to describe total and differential cross sections of proton-proton interaction in wid eenergy regions.     

On a Model of Random Cycles

We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with infinite, macroscopic cycles.     

Spherical Model in a Random Field

We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field. We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable, but it self-averages conditionally. We also show that an arbitrarily weak homogeneous boundary field dominates over fluctuations of the random field once the model transits into a ferromagnetic phase. As a result, a homogeneous boundary field restores the conventional self-averaging of thermodynamic observables, like the magnetization and the susceptibility. We also investigate the effective field created at the sites of the lattice by the random field, and show that at the critical temperature of the spherical model the effective field undergoes a transition into a phase with long-range correlations ∼r ^4−d .     

Quantum Entanglement in a Generic-Spin Model

We investigate quantum entanglement in a generic-spin model with spin squeezing criterions based on squeezing inequalities. By analytically and numerically calculating the squeezing criterions, we show that the system is always entangled except at some special times and the stronger entanglement may be achieved by decreasing the coupling strength and increasing the number of particles.