物理公式教学"一、二、三"

物理教学中，常发现学生滥用或死套公式，无法正确地求解物理问题．因此，搞好公式教学是提高物理教学质量的关键．笔者结合多年的教学体会，总结出关于公式教学的“一个理解、二个掌握、三个注意”，经实践检验，效果很好，供同行们参考．     

原子核转动谱公式的回顾与比较

回顾和比较了原子核转动谱的几个常用公式, 对目前已观测到的正常变形和 超变形转动带的分析表明, 二参数ab公式和三参数abc公式是参数数目相同的公式中与实验符合得最好的公式, 可供实验工作者方便采用.     

具有三个二次曲面反射镜的光学系统研究

本文从三级像差理论导出了三镜系统消S_Ⅰ、S_Ⅱ、S_Ⅲ、S_Ⅳ的代数解.以第二及第三镜的遮拦比和放大率,以及三个镜面的面形系数为独立参数,结出消像差条件公式.用国外发表的几个三镜系统验证这些公式,得到很好的吻合.     

空间散斑的运动规律

相干光照明的漫射表面在空间中产生随机散斑。反射表面相对于光源运动,引起散斑的相应运动。当跟踪一个运动的斑,认为斑的强度不变,而位相是可以变化的。从Fresnel-Kirch-hoff积分,得到关于散斑运动的三个基本规则,即文中的(3),(4)和(5)式。第一和第二式类似于光栅方程。第三式类似于透镜定律。从这三个规则推导了当表面运动时散斑的运动公式(18)。这公式以矩阵形式表示,包括三个转动和三个平动。实验结果与公式非常符合。同时,三个基本规则适用于一般的空间衍射图。 关键词：     

Bohr—Mottelson公式对超形变带的比较研究：？…

用Ｂｏｈｒ－Ｍｏｔｔｅｌｓｏｎ的两参数、三参数和四参数公式对Ａ～１９０区６１条超形变带进行了系统分析。结果显示：３个公式都能较好地拟合１９０区超形变带的Ｅ２跃迁谱,而且带自旋的确定基本一致。大部分带Ｂｏｈｒ－Ｍｏｔｔｅｌｓｏｎ的三参数数值关系符合ａｂ公式的理论预期值,小部分带的三参数值关系符合Ｈａｒｒｉｓ公式的理论预期值,一半以上带的四参数数值关系与ａｂ公式的预期值接近,而与Ｈａｒｒｉｓ公式的预期     

两个新的单摆周期公式

本文提出两个新的单摆周期公式与原有公式相比，它们都具有简单实用的优点．其中第二个新公式，还以简洁的方式表明了单摆周期与最大摆角间的函数关系，具有一定的理论价值．     

引力定律的新研究

本文第一部分提出一种数学模式；切线变换，用这一数学模式研究曲率半径的公式及圆锥曲线的性质，第二部分用切线变换重新研究牛顿的万有引力定律，推导出天体运行统一的能量方程和离心率公式，第三部分应用切线变换由行星轨道进动推导出引斥力公式，并推导出相应的能量方程和离心率公式。     

海底沉积物声速与物理性质的理论关系

为建立海底沉积物声速与物理性质的关系,引入密度变化比和弹性模量变化比为参数描述海底沉积物声速。密度变化比是描述声速的一个复合参数,由孔隙率、固相密度和海水密度三个物理参数表示;弹性模量变化比是描述声速的另一个复合参数,由孔隙率、固相体积模量和海水体积模量三个物理参数表示;声速公式可展开为这两个复合参数的泰勒多项式。两个复合参数的变化构成声速曲面,声速曲面包含了声速特性与沉积物性质的完整信息;而单参数声速公式是声速曲面上的一条曲线。数值计算与测试结果对比表明:把孔隙率-声速经验公式变换为参考声速乘以一个调制函数的标准形式,各个海区的孔隙率-声速经验公式的调制函数是相当接近的。论文导出的声速公式与Wood声速公式的区别在于弹性模量的模型不同。      

海底沉积物声速与物理性质的理论关系

为建立海底沉积物声速与物理性质的关系,引入密度变化比和弹性模量变化比为参数描述海底沉积物声速。密度变化比是描述声速的一个复合参数,由孔隙率、固相密度和海水密度三个物理参数表示;弹性模量变化比是描述声速的另一个复合参数,由孔隙率、固相体积模量和海水体积模量三个物理参数表示;声速公式可展开为这两个复合参数的泰勒多项式。两个复合参数的变化构成声速曲面,声速曲面包含了声速特性与沉积物性质的完整信息;而单参数声速公式是声速曲面上的一条曲线。数值计算与测试结果对比表明:把孔隙率-声速经验公式变换为参考声速乘以一个调制函数的标准形式,各个海区的孔隙率-声速经验公式的调制函数是相当接近的。论文导出的声速公式与Wood声速公式的区别在于弹性模量的模型不同。     

相互作用能、势能以及极化状态改变作功

指出在一般教学参考书中给出的静电场互作用能公式，仅仅是电势能公式，两个带电物体间的相互作用能，除了势能以外，还应包括由于相互极化导致物体极化导致物体状态改变所作的功和外电源提供的能量，本导出了两个带电物体间相互作用能的普遍公式。     

双波量子理论中的守恒定律

研究了双波量子理论中守恒定律的数学形式,讨论了三维各向同性谐振子的守恒量及其经典极限.结果表明,双波量子理论中的守恒定律适用于单个粒子,而通常量子力学中的守恒定律仅适用于统计系综. 关键词：     

超微球透镜的耦合效率极限

本文从像差理论入手,分析了一种超微型透镜光学耦合系统的耦合理论问题,得出了可用作推算这种光学耦合系统耦合效率极限的计算公式。这组公式较Nicia导出的公式更具广泛的适用性,且可推广使用在一般透镜光纤耦合系统的分析之中。文中还给出了具体的计算实例和实验结果。     

An analysis of binary flutter of bridge deck sections

This paper is concerned with an analytical and experimental study of binary flutter of bridge deck sections. A set of analytical formulas giving the frequency and rate of growth of oscillation, the position of the equivalent center of rotation and the phase difference between bending and torsion near the critical flutter point is presented. The formulas provide an analytical basis for the previously proposed method of classification of binary flutter of bluff structures. The results of wind tunnel experiments on models with simple geometrical shapes confirm that the present formulas are applicable to a variety of structures ranging from a flat plate to much more bluff bridge deck sections.     

A new approximate analytical approach for dispersion relation of the nonlinear Klein-Gordon equation

A novel approach is presented for obtaining approximate analytical expressions for the dispersion relation of periodic wavetrains in the nonlinear Klein-Gordon equation with even potential function. By coupling linearization of the governing equation with the method of harmonic balance, we establish two general analytical approximate formulas for the dispersion relation, which depends on the amplitude of the periodic wavetrain. These formulas are valid for small as well as large amplitude of the wavetrain. They are also applicable to the large amplitude regime, which the conventional perturbation method fails to provide any solution, of the nonlinear system under study. Three examples are demonstrated to illustrate the excellent approximate solutions of the proposed formulas with respect to the exact solutions of the dispersion relation. (c) 2001 American Institute of Physics.     

Energy characteristics of oscillatory systems with internal (Hidden) degrees of freedom

The general formulas are derived for calculating the kinetic and potential energies and other energy characteristics of linear oscillatory systems, a portion of the degrees of freedom of which are internal, i.e., inaccessible for direct measurements and/or excluded from consideration. The energy characteristics are expressed by means of parameters pertaining only to the part of accessible (or selected for consideration) degrees of freedom. The formulas are derived based on the use of certain novel properties of the so-called Shur matrix complement. The obtained formulas are applicable for calculating the energy characteristics of the elements of acoustic metamaterials by means of their effective inertial-elastic parameters. The main focus is the case of negative values of these parameters. Proceeding from the nonnegativity of the kinetic and potential energies of mechanical structures, limitations on the character of the frequency dependences of the effective parameters are formulated.     

Extreme statistics of complex random and quantum chaotic states

Complex random states have the statistical properties of the Gaussian and circular unitary ensemble eigenstates of random matrix theory. Even though their components are correlated by the normalization constraint, it is nevertheless possible to derive compact analytic formulas for their extreme values' statistical properties for all dimensionalities. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulas.     

Classical Skew Orthogonal Polynomials and Random Matrices

Skew orthogonal polynomials arise in the calculation of the n-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely determined by a certain sum involving the skew orthogonal polynomials. In the case that the eigenvalue probability density function involves a classical weight function, explicit formulas for the skew orthogonal polynomials are given in terms of related orthogonal polynomials, and the structure is used to give a closed-form expression for the sum. This theory treates all classical cases on an equal footing, giving formulas applicable at once to the Hermite, Laguerre, and Jacobi cases.     

Calculation of thermoelastic stresses near the crystallization front for melt-grown single-crystal rods with a circular cross section

Approximate expressions for the thermoelectric stress tensor components in an isotropic crystal rod of a circular cross section, applicable in the entire crystal including the region near the crystallization front, are obtained. Using the resultant approximate formulas, the stress fields in leucosapphire single crystals are calculated for model temperature fields. It is shown that exactly near the crystallization front, thermoelastic stresses reach maximal values.     

The quantum theory of the radiation from charged polarized fermions moving in crossed fields

The radiation of a charged Dirac particle, moving at relativistic velocity in orthogonal electric and magnetic fields (E H), is examined here. The formulas obtained are applicable for arbitrary orientation of the particle spin.     

Electric field distribution in an electroluminescent cell

The theory of linear parameter distribution is discussed in relation to calculation of the intensity for an electroluminescent cell (EC). It is found that some of the formulas are applicable to the practical ranges of EC because the spatial region where nonlinear processes occur in strong fields is of restricted extent.Read at the 14th All-Union Conference of Luminescence (Crystal Phosphors), 20 September 1965.