变参数体系自由振动初值问题新解法

本指出一类广泛的变参数体系的自由振动方程可以写成x^·（t)=A(t)X(t)，式中A(t)是一个半单线性算子其全部特征值都是纯虚数。对这类方程（量子力学中的Schroedinger方程是其特例），在A(t)变化缓慢的假定下，本提出了一种普适解法，把问题归为求解A（t)的特征方程。只要知道A（t)的特征值和特征向量，就可以写下上述方程初值问题的解，达到任意精确程度。

A New Approach for Solving Initial Value Problems of Free Vibration of Systems with Varying Parameters

It is shown that the free vibration equation of a wide variety of systems with varying parameters can be written as X(t)=-A(t)X(t),where A(t)is a semisimple linear operator and all its eigenvalues are pure imaginary.A new approach to such kinds of equations,which include Schr(?)dinger equations in Quantum Mechanics as special ex- amples,is proposed under the assumption that A(t)varies slowly with time.By using it,the solution to the initial problem with any desired accuracy can be readily written down,only if all the eigenvalues and eigenvectors of A(t)are known.