普通物理力学与理论力学教学的衔接

以经典力学的产生和发展为背景,评价普通物理力学和理论力学课程的衔接,从教学目的、教学内容、方法特点和难度要求等四个方面分析教学衔接问题的要点。     

巧用类比教学法实现刚体力学的有效教学

巧妙地运用类比教学法对刚体力学和质点力学的物理概念、物理规律、公式以及解决问题的思路和方法等方面列表逐一分析、探究。部分测验成绩表明,巧用类比教学法,能提高刚体力学部分学业成绩,从而实现了刚体力学的有效教学。     

中学力学问题求解的两大途径

多年教学经验告诉我,在力学部分,学生在认真审题、确定研究对象、分析物理过程以后,对如何选用物理规律、公式,分析问题、建立方程求解,普遍感到困惑.     

力学教学改革探索

普通物理中的力学部分一直是较难处理的内容，自然也就成为大家所关注的问题，近几年我在这方面做了一些改革；例如以三大力学守恒定律作为内容的主线，对力学的课时进行了大幅度的削减，目前仅用10-11小时，基本上做到了使教学内容与中学不重复，     

关于分析力学中势能的一个注记

指出了理论力学教材中分析力学部分关于势能与力的关系的一点不足之处,具体讨论了势能的表示式.     

巧用类比教学法实现刚体力学的有效教学简

巧妙地运用类比教学法对刚体力学和质点力学的物理概念、物理规律、公式以及解决问题的思路和方法等方面列表逐一分析、探究。部分测验成绩表明,巧用类比教学法,能提高刚体力学部分学业成绩,从而实现了刚体力学的有效教学。     

大学生物理竞赛试题赏析（Ⅰ）--力学部分

首先对全国部分地区大学生物理竞赛中力学试题所占的比例进行统计,然后分析力学试题中各知识点的分布情况,最后就两个典型的力学试题进行剖析。     

力学综合课程建设的研究和实践

简述了我校物理系进行力学综合课程建设的基本思想和措施，以及建立将普通物理力学、理论力学和量子力学基础综合成一门课程的新的教学内容结构体系的具体做法．这样做，不但大大减少了重复内容和课时。而且有助于学生从整体上把握力学理论的基本框架，有助于培养学生的综合研究能力和创新能力。     

基于对比学习的分析力学教学方案——以两个典型物理问题为例

针对分析力学教学环节中学生普遍存在的问题，本文从2个典型的物理问题——降落伞与双摆模型入手，通过一题多解与对比学习的形式，呈现2种力学在处理相同物理问题时的差异.引导学生思维从经典牛顿力学向分析力学过渡，使其能够尽快融入到分析力学的学习中去.同时在教学过程中引入适当的数值计算，进一步加深学生对具体物理问题的理解.     

热振动在纳米力学测量中的应用

基于能量均分定理和悬臂梁理论,分析讨论了微悬臂梁进行热振动的物理模型。通过三个实例,介绍了热振动在纳米力学测量中的应用,其中重点阐述了单根纳米晶须的杨氏模量的热振动定量测量方法。     

Bohmian mechanics to high-order harmonic generation

This paper introduces Bohmian mechanics (BM) into the intense laser-atom physics to study high-order harmonic generation. In BM, the trajectories of atomic electron in an intense laser field can be obtained with the Bohm--Newton equation. The power spectrum with the trajectory of an atomic electron is calculated, which is found to be irregular. Next, the power spectrum associated with an atom ensemble from BM is considered, where the power spectrum becomes regular and consistent with that from quantum mechanics. Finally, the reason of the generation of the irregular spectrum is discussed.     

Fractals and quantum mechanics

A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Levy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics. (c) 2000 American Institute of Physics.     

力学概念理解和问题解决能力的调查研究

首先介绍Hestences等人开发的MBT(mechanics baseline test)——力学基准测试题目,并且对北京师范大学物理系一年级学生进行了测试,把测试的结果和美国的有关研究结果进行了分析和比较．接着通过一个现实生活中的问题来分析学生解决实际问题的能力,发现教学中存在的问题．最后对我们目前的教学情况进行了评述．     

Functional analysis and quantum mechanics: an introduction for physicists

We give an introduction to certain topics from functional analysis which are relevant for physics in general and in particular for quantum mechanics. Starting from some examples, we discuss the theory of Hilbert spaces, spectral theory of unbounded operators, distributions and their applications and present some facts from operator algebras. We do not give proofs, but present examples and analogies from physics which should be useful to get a feeling for the topics considered.     

Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics

From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equations) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern mechanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.     

创立量子力学的睿智才思(续2)——纪念矩阵力学和波动力学诞生80～81周年

1922年前后玻尔-索末菲的旧量子论在原子结构理论上取得辉煌成就的同时，它的致命弱点也开始暴露出来．反常塞曼效应是其一，原子光谱的多重线结构是其二，更不要说氢分子离子H2^＋问题了．一时多少杰出的物理学家为这些问题绞尽脑汁，设计了各种物理模型，提出一些“代用（德文Er-satz）”理论，诸如海森伯和泡利的Zwang之类，到头来还只得愁眉以对，一筹莫展．无怪乎海森伯把反常塞曼效应叫做“光谱项的动物学和塞曼植物学（Term Zoology and Zeeman Botany）”，意即在这个领域里物理学家只能像生物学家那样记录现象和描绘事实，提不出像样的理论．到1925年下半年，人们手里有了矩阵力学，问题是否可以解决了呢？万事俱备，只欠“东风”，那就是“自旋”．     

Classical limit of scattering in quantum mechanics—A general approach

The classical and quantum physics seem to divide nature into two domains macroscopic and microscopic. It is also certain that they accurately predict experimental results in their respective regions. However, the reduction theory, namely, the general derivation of classical results from the quantum mechanics is still a far cry. The outcome of some recent investigations suggests that there possibly does not exist any universal method for obtaining classical results from quantum mechanics. In the present work we intend to investigate the problem phenomenonwise and address specifically the phenomenon of scattering. We suggest a general approach to obtain the classical limit formula from the phase shiftδ _l, in the limiting value of a suitable parameter on whichδ _l depends. The classical result has been derived for three different potential fields in which the phase shifts are exactly known. Unlike the current wisdom that the classical limit can be reached only in the high energy regime it is found that the classical limit parameter in addition to other factors depends on the details of the potential fields. In the last section we have discussed the implications of the results obtained.     

对突破工科近代物理教学一个瓶颈问题的探讨

在工科近代物理教学中,量子力学部分所占比例非常少,而量子力学基础教学中的一个瓶颈在于算符和算符本征值与力学量概率分布的关系.介绍了为突破这一瓶颈,在教材建设和教学实践中所做的改进.     

Everettian quantum mechanics

ABSTRACT

An interpretation of quantum mechanics dating back to mid-1950s, based on the ideas of Hugh Everett III, has found a new lease on life in recent decades. Significant efforts have been made by physicists and philosophers of physics to bring advances in physics and philosophy to bear on the interpretation, and to overcome some of the shortcomings in Everett's bold, but limited writings. This article presents an introduction to Everettian quantum mechanics.