正则变换与二粒子耦合体系哈密顿量的对角化技术

把耦合项为Ｃ（ａ＾１ａ２＾＋ａ２＾＋ａ１）＋Ｄ（ａ＾＋１ａ＋２＋ａ２ａ１）的Ｈａｍｉｌｔｏｎ量写成超矩阵相乘的形式，通过正则变换使其对角化。     

幺正变换与二粒子耦合体系Hamilton量的对角化技术

本文给出耦合项为Ｂｉ（ａ１＾＋ａ２＾＋－ａ２ａ１）＋Ｃｉ（ａ１＾＋ａ２－ａ２＾＋ａ１）Ｈａｍｉｌｔｏｎ量的解耦合方法，可作为笔者在《大学物理》１９８９年第６期和１９９３年第５期上所发表的两篇文章的续篇。     

二元线性回归方程中系数a0的偏差讨论

本文讨论了根据最小二乘法原理拟合二元线性回归万程ｙ＝ａ０＋ａ１ｘ１＋ａ２ｘ２时，得到的估计值ａ０、ａ１和ａ２都是和ｙｉ有关的量，并推导得到系数ａ０的标准偏差的正确表达式．     

A3M2Ge3O12石榴石体系中Cr3+离子的宽带发射光谱

首次报告在Ａ３Ｍ２Ｇｅ３Ｏ１２∶Ｃｒ（Ａ＝Ｃｄ２＋,Ｃａ２＋;Ｍ＝Ａｌ３＋,Ｇａ３＋,Ｓｃ３＋）锗酸盐石榴石体系中,Ｃｒ３＋离子室温下的红—近红外（Ｒ—ＮＩＲ）宽发射带光谱性质。随位于八面体格位上的Ａｌ３＋→Ｇａ３＋→Ｓｃ３＋和十二面体格位上的Ｃｄ２＋→Ｃａ２＋组成顺序变化,室温下,Ｃｒ３＋离子的４Ｔ２→４Ａ２能级跃迁的Ｒ－ＮＩＲ宽发射带,发射峰及光谱的长波和短波边逐渐向低能长波边移动。这是由于晶场强度减弱,阳离子的离子半径增大的结果。在镉（钙）铝和镉（钙）镓锗酸盐体系中,少量Ｓｃ３＋取代八面体上的Ａｌ３＋和Ｇａ３＋时,可使Ｃｒ３＋的Ｒ－ＮＩＲ荧光发射强度增强。     

叠加q相干态的振幅M次方压缩

本文构造了以奇偶ｑ相干态为特例的一般叠加ｑ相干态｜α,θ〉ｑ＝ｃ（｜α〉ｑ＋ｅ＾ｉθ｜－α〉ａ）,并研究了它的振幅Ｍ次方压缩性质,发现这种叠加态只存在振幅奇数次方压缩效应。并数值计算了叠加系娄籴形参数对压缩的影响。     

中专物理教学中的数学应用

物理学是研究物体运动及其规律的科学,许多物理学上的难题借助于数学推论得到了解决,对此,我谈谈自己在中专物理教学中的体会．１　极值问题常用求极值的数学方法：（１）重要不等式求极值：例如：ａ＋ｂ≥２ａｂ　（或　ａ２＋ｂ２≥２ａｂ）ａ＞０　ｂ＞０若ａ＋ｂ为一常量,则当且仅当ａ＝ｂ时,ａ＋ｂ有极大值．若ａ·ｂ为一常量,则当且仅当ａ＝ｂ时,ａ＋ｂ有极小值．（２）函数求极值：利用正、余弦函数、二次函数及某些特殊函数求极值．下面举例说明数学原理在求物理量极值中的应用．例１,点光源Ｓ到屏Ｍ的距离为Ｌ．焦距为ｆ的…     

依赖于时间的Jaynes—Cummings模型中的反聚束效应

本文利用友格－库塔法对多个方程组连续进行积分，提出了一种处理依赖于时间的Ｊａｎｅｓ－Ｃｕｍｍｉｎｇｓ模型，描述二能级原子与腔场相互作用的耦合系数依赖于时间的ＪＣＭ的哈密顿量为Ｈ＝１／２ω０σ３＋ω＾＋ａ＾＋ａ＾＋ｇ（ｔ）（σ＋ａ＋σ－ａ）ｈ＝１（１）这里，ｇ（ｔ）选择为时间上的一个脉冲ｇ（ｔ）＝ｇ０ｅｘｐ（－（ｔ－ｔ０）＾２／２ａ＾２），其中ｔ０和ａ分别为脉冲中心和脉冲宽度，ｇ０是一有量纲常数，     

A3M2GeO12石榴石体系中Cr^3＋离子的宽带发射光谱

首次报道在Ａ３Ｍ２Ｇｅ３Ｏ１２：Ｃｒ（Ａ＝Ｃｄ＾２＋,Ｍ＝Ａｌ＾３＋,Ｇａ＾３＋,Ｓｃ＾３＋）锗酸盐石榴石体系中,Ｃｒ＾３＋离子室温下的红－近红外宽发射带光谱性质。随位于八面体格位上的Ａｌ＾３＋→Ｇａ＾３＋→Ｓｃ＾３＋和十二面体格位上的Ｃｄ＾２＋→Ｃａ＾２＋组成顺序变化,室温下,Ｃｒ＾３＋离子的＾４Ｔ２→＾４Ａ２能级跃迁的Ｒ－ＮＩＲ宽发射带,发射峰及光谱的长波和短波边逐渐向低能长波边移动。     

分子束反应动态学及分子传能研究

本文扼要介绍了中国科学院大连化学物理研究所分子束反应动态学及分子传能课题组自１９７９年以来研究工作概况，井对 Ｂａ ＋ Ｃｌ２反应产生 ＢａＣｌ２＊的机理、Ｂａ＋Ｎ２Ｏ反应机理、Ｓｎ＋Ｎ２Ｏ反应机理、Ｃ＿２ｄ＿３态在 Ｎａ＋ ＣＣｌ４反应中生成机制和能量传递过程及碱土金属原子与卤代烷反应中反应产物的能量配置规律作了简要的说明．     

CaS:Cu~+,Eu~(2+)的光致发光及其在农业生产中的应用

研究了Ｃｕ＋，Ｅｕ２＋共激活的ＣａＳ的发光性质及激活剂浓度与荧光性质的关系．Ｃｕ＋和Ｅｕ２＋的发射光谱分别在４３０ｎｍ附近及６３０ｎｍ附近，它们是由Ｃｕ，Ｃａ－Ｖｓ２＋中心的离子发射和Ｅｕ２＋的５ｄ－４ｆ跃迁发射产生的．实验结果表明，Ｃｕ＋对Ｅｕ２＋荧光发射有较强的敏化作用，Ｅｕ２＋对Ｃｕ＋发射峰值波长和强度也有显著影响；单掺Ｅｕ２＋或Ｃｕ＋的荧光粉是良好的农用薄膜红，蓝光转换剂，共掺Ｅｕ２＋和Ｃｕ＋的ＣａＳ荧光粉作光转换农膜添加剂可望人工模拟叶绿素的吸收光谱，使作物在植物最佳生长作用光谱环境中生长，促使作物早熟或提高作物产量     

Fast sweeping method for the factored eikonal equation

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss–Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss–Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.     

一类Landau-Ginzburg-Higgs扰动方程孤子的近似解

利用解析方法研究了一类Landau-Ginzburg-Higgs方程. 由广义变分迭代理论得到了相应方程的解,从而得到了对应方程孤子的近似解. 关键词： 孤子 扰动 变分迭代     

A fast method for the solution of the Helmholtz equation

In this paper, we consider the numerical solution of the Helmholtz equation, arising from the study of the wave equation in the frequency domain. The approach proposed here differs from those recently considered in the literature, in that it is based on a decomposition that is exact when considered analytically, so the only degradation in computational performance is due to discretization and roundoff errors. In particular, we make use of a multiplicative decomposition of the solution of the Helmholtz equation into an analytical plane wave and a multiplier, which is the solution of a complex-valued advection–diffusion–reaction equation. The use of fast multigrid methods for the solution of this equation is investigated. Numerical results show that this is an efficient solution algorithm for a reasonable range of frequencies.     

Explicit N-Solit on Solution of the Unstable Nonlinear Schrödinger Equation

The unstable nonlinear Schrodinger (NLS) equation is solved by the inverse scattering transform. Based on the constructed Zakharov-Shabat equation, it is shown that the soliton solution of the unstable NLS equation can be known from the soliton solution of the usual NLS equation by simply exchanging the tariables. The explicit N-soliton solution and the position shifts due to the collision are thus calculated.     

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper.The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope.The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation.The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope.The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly,which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope.The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained,which provides a reference for the robust design of the resonant gyroscope.     

Infinite series symmetry reduction solutions to the modified KdV--Burgers equation

From the point of view of approximate symmetry, the modified Korteweg--de Vries--Burgers (mKdV--Burgers) equation with weak dissipation is investigated. The symmetry of a system of the corresponding partial differential equations which approximate the perturbed mKdV--Burgers equation is constructed and the corresponding general approximate symmetry reduction is derived; thereby infinite series solutions and general formulae can be obtained. The obtained result shows that the zero-order similarity solution to the mKdV--Burgers equation satisfies the Painlevé II equation. Also, at the level of travelling wave reduction, the general solution formulae are given for any travelling wave solution of an unperturbed mKdV equation. As an illustrative example, when the zero-order tanh profile solution is chosen as an initial approximate solution, physically approximate similarity solutions are obtained recursively under the appropriate choice of parameters occurring during computation.     

An alternative derivation of the pulse solutions of the KdV hierarchy

An alternative approach issues from the Appelle transformation of the Schrödinger equation. One solves the inverse problem for the transformed equation, a general solution of which is a quadratic form of two independent solutions of the primary Schrödinger equation. If the potential in the Schrödinger equation obeys one equation of the KdV hierarchy, the time derivative of this form is a linear combination of the form and its space derivative. The coefficients in the combination depend on the potential and the energy parameter of the Schrödinger equation only. This relation also determines the time dependence of the spectral data which along with the solution of the inverse problem gives the solution of the KdV equations as usual.     

The effect of the heat capacity of the liquid phase on the heat of fusion liquidus equation of compound semiconductors

We have critically examined the assumptions involved in the derivation of Vieland's widely used heat of fusion liquidus equation for binary compounds and conclude that the thermodynamic form of this equation ignores the relative partial molar heat capacity of the liquid solution. Taking into account this quantity, we obtain the generalized heat of fusion equation which is exact and show its complete equivalence to its alternative, the heat of formation equation. The generalized result provides a correction term to Vieland's equation which can be expressed as a function of the activity coefficients at the compound composition. Applying the correction term to the activity coefficients derived for a number of useful solution models, we find that the regular solution form of Vieland's equation is exact, as shown previously, if α (interchange energy) is a constant or a linear function of temperature. But when α is expanded as an nth order polynomial in temperature (simple solution), Vieland's equation is inexact for n ? 2. In addition, it is demonstrated that for a regular associated solution and for Darken's quadratic representation, Vieland's thermodynamic equation is exact only with certain restrictions, while for a quasi-chemical solution it is invalid.     

An Exact Solution to the Two-Particle Boltzmann Equation System for Maxwell Gases

An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given.     

A method of obtaining the N-soliton solution of the Boussinesq equation in terms of a wronskian

By means of a Bäcklund transformation for the Boussinesq equation in bilinear form, the wronskian form of the N-soliton solution of that equation is deduced. The solution is then verified by direct substitution in the equation.