乔治·格林及格林函数法

乔治.格林是一位重要的数学物理学家.简要介绍了乔治.格林的生平和科学研究经历,揭示了帮助他取得重要科学研究成果的主要因素,介绍了格林函数法的建立过程及其重要性.     

环形振子势的精确解

将环形振子势的Schrödinger方程在球坐标系中进行变量分离.然后求解了角向方程和径向方程,给出了精确的能谱方程.获得了用普遍的缔合Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数.     

格林方程的新推导

微分几何理论导出了格林方程．     

格林函数的有限形式法中微分方程之解的证明

本文通过对静电场格林函数分离变量得到非齐次常微分方程，判断其解及解存在的条件，完善了电动力学［１］提到的格林函数的有限形式法．     

有限精度函数理论与Einstein-Maxwell方程的光子解

提出了有限精度函数理论,并基于该理论求出了有限精度的Einstein-Maxwell方程的光子解,揭示了经典光子的电磁、引力与时空几何的重要性质. 关键词： 有限精度函数理论 Einstein-Maxwell方程 光子解     

多体关联Green函数动力学Ⅰ多体关联Green函数的运动方程

从多体系统的哈密顿量及海森堡方程出发,通过引进非线性变换,完成了体系的多体Green函数的关联分离,并建立起非相对论性的多体关联Green函数的动力学方程组.这个方程组为描述多体系统提供了一种完整的、系统的非微扰计算方法.     

镍晶格中的晶格格林函数

在含缺陷体系的模拟中，格林函数作为一种重要的多尺度耦合方法，可以将缺陷产生的局域应变场和长程应力场耦合起来.在镍基高温合金蠕变的初期阶段，位错主要分布在基体相中，通过格林函数的多尺度桥接模式，可得到基体相中位错芯的平衡构型，为位错-杂质复合体间相互作用提供计算基础.基于晶格动力学理论和声子谱计算中的力常数矩阵，通过第一布里渊区特殊k点取样以及傅里叶变换，计算完整镍晶格中晶格格林函数，可用于镍基材料的多尺度模拟计算.     

非线性单摆的格林函数解法

应用格林函数方法,给出了非线性单摆运动的较好近似解．     

广义振子势的精确束缚态解

本文求解了广义振子势在r,θ,φ方向上的Schrǒdinger方程,得到了它的能级和相应的归一化角向、径向波函数.利用广义拉盖尔多项式的积分公式得到了广义振子势的径向矩阵元的通向表达式.     

用变分法解Fokker—Planck方程计算核裂变几率

发展了一种用变分法解Fokker-Planck方程的方法,计算了一维核裂变几率,研究了F-P方程与Smoluchowski方程的关系,为推导多维的质量系数和粘滞系数随形变参量变化并具有交叉项的Smoluchowski方程和解位能形式比较复杂的多维的F-P方程打下了基础.     

Analysis of modified Van der Pol’s oscillator using He’s parameter-expanding methods

In this work, a powerful analytical method, called He’s parameter-expanding methods (HPEM) is used to obtain the exact solutions of non-linear modified Van der Pol’s oscillator. The classical Van der Pol equation with delayed feedback and a modified equation where a delayed term provides the damping are considered. It is shown that one term in series expansions is sufficient to obtain a highly accurate solution, which is valid for the whole solution domain. Comparison of the obtained solution with those obtained using perturbation method shows that this method is effective and convenient to solve this problem. This method introduces a capable tool to solve this kind of non-linear problems.     

Solitary Solution of Discrete mKdV Equation by Homotopy Analysis Method

In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows that homotopy analysis method is effective and validity in solving hybrid nonlinear problems, including solitary solution of difference-differential equation.     

范德瓦尔斯方程的分子平均场理论推导

利用气体分子动理论和分子平均场理论,导出了真实气体物态方程--范德瓦尔斯方程,并与统计力学严格的理论推导结果作比较,得到了反映真实气体分子作用域大小的一个较为具体的参考值.     

范德瓦耳斯气体体积修正的新计算方法

范德瓦耳斯方程能够较好地描述实际气体的热力学过程,方程中的参数b是因实际气体分子的体积而引入的修正量.本文通过考察分子之间的相互碰撞事件,计算得到了范德瓦耳斯气体体积的修正值,约等于1 mol气体所有分子体积总和的4倍,结果与其他方法得到的结果一致.这是一种新的计算思路和方法.     

Integral kinetic method for one dimension: The spherical case

The integral method to numerically calculate the time evolution of kinetic systems is discussed and improved for one-dimensional problems. The new approach is applied to the solution of the spherically symmetric one-component plasma kinetic evolution. The results are compared with those obtained by means of the finite-difference solution to the equivalent Fokker-Planck kinetic equation.     

N-Soliton-like Solution of Ito Equation

By using the extended Hirota‘s method, the N-soliton-like solution of the Ito equation is obtained. Furthermore, we also investigate the soliton-like solution interaction and find singularity.     

N-Soliton-like Solution of Ito Equation

By using the extended Hirota‘s method, the N-soliton-like solution of the Ito equation is obtained. Furthermore, we also investigate the soliton-like solution interaction and find singularity.     

Solution of Dirac Equation with Killingbeck Potential by Using Wave Function Ansatz Method under Spin Symmetry Limit

The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.     

Solution of Dirac Equation with Generalized Hylleraas Potential

We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formalism of the Dirac equation with a generalized Hylleraas potential of the form V(r) = V0(a+exp(λr))/(b+ exp(λr)) + V1(d+exp(λr))/(b+exp(λr)).We obtain the bound state energy eigenvalue and the corresponding eigenfunction expressed in terms of the Jacobi polynomials.By choosing appropriate parameter in the potential model,the generalized Hylleraas potential reduces to the well known potentials as special cases.