算子方程

Two basic theorems are given by researching Hamilton's two steps linear differential equations of bender equations which provide widespread application methods of normal differential operator correspond to ladder operators,then the solutions of general equations are obtained by taking advantage of the two above theorems: The energy eigenvalue equation of one-dimensional oscillator; the common state of ; the radial equation of a bondage state of hydrogen atom; the radial equation isotropic three-dimensional harmonic oscillator; the infinity deep potential well of ball

本文通过研究束缚态本征方程里的哈密顿算符的二阶线性常微分形式，给出两个基本定理并证明，提供构造二阶线性常微分算符相应的阶梯算符的普遍实用的方法，然后利用这两个定理构造量子力学中常见力学量的阶梯算符，并用以计算其能量本征值和对应本征函数：一维谐振子的能量本征方程；共同本征态；氢原子束缚态径向方程；三维各向同性谐振子的径向方程；无限深球势阱。

We prove the existence of integral solutions for semilinear integrodifferential equations with nonlocal conditions in Banach spaces.

运用预解算子理论和Schauder不动点定理，在Banach空间证明了一类非局部半线性积微分方程积分解的存在性。

This chapter deals with the existence of mild and strong solutions of a nonlinear integrodifferential systems of Sobolev type with nonlocal condition in Banach spaces.

本章在Banach空间中，用算子半群理论以及Schauder不动点定理讨论了一类非线性Sobolev型积分微分方程，在非局部初始条件下，适度解和强解的存在性。

Only the system of primary interest needs to be considered microscopically.

原则上，利用投影算子法或Feynman路径积分，我们可以严格写出量子耗散动力学方程。

In the last part, we study the existence of the solutions for semilinear subelliptic equations and the estimates of the eigenvalues for subelliptic operators on H.

另外我们还研究了Heisenberg群上一类半线性次调和方程的解的存在性问题及Heisenberg上群一类次调和算子的特征值估计问题。

For the case of waveduide R~2×M, where M be Zoll manifolds, if the initial data is small enough, we can use the special distribution of eigenvalues of Laplace-Beltrami operator on Zoll manifold, the estimate of the energy and the technique of normal form to prove the existence of global solutions for nonlinear Klein-Gordon equations.

对波管R~2×M上的非线性Klein-Gordon方程，其中M为Zoll流形，如果初值足够小，利用Zoll流形上Laplace-Beltrami算子的特征值的分布，并结合能量估计和法形式技巧，我们证明了整体解的存在性。

With degenerate approximations to the oneway LippmannSchwinger integral equation, we study a category of wideangle degenerate migrators that permit the implementation of seismic migration using fast Fourier transforms alone.

通过对LippmannSchwinger单程波动积分方程的退化核逼近，本文研究了一类宽角退化算子的偏移成像。

Wideangle parabolic approximations to wave equation usually lead to nonconstant differential migrators with their coefficients varying with lateral velocity variations, and hence require a finitedifference numerical implementation.

波动方程宽角抛物逼近得到的通常是非常系数的单程波传播算子，其系数是速度横向变化的函数，因此需要利用有限差分进行数值实施。

The analyticity of the propagators for higher order equations ina Banach space is studied,and a characterization is obtained.

研究Banach空间中高阶方程传播算子的解析性，获得一个特征刻划。

For certain initial conditions,we need only calculate their high order Laplace operator,then we can obtain the accurate solution of the initial value problem.

本文提供了一种算法，对某些初始条件，只需计算其高阶拉普拉斯算子，就可以得到方程的显解。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。