一维随机势薛定谔方程本征函数局部化度的谱依赖性
Spectral Dependence of Degree of Localization of Eigenfunctions of the 1D Schrodinger Equation with a Peacewise-Constant Random Potential
摘要：
本文发展了具有分段常数随机势的一维薛定谔方程超前和滞后格林函数联合统计的微扰理论。使用这种方法，解析表达式得到的光谱依赖的程度的本地化和限制（在$t\rightarrow\infty$）的概率找到粒子的点，它位于$t = 0$（安德森准则）。介绍了局部化长度的定义。计算机实验证实了计算的正确性。
英文摘要：
The perturbation theory is developed for joint statistics of the advanced and retarded Green's functions of the 1D Schrodinger equation with a piecewise-constant random potential. Using this method, analytical expressions are obtained for spectral dependence of the degree of localization and for the limiting (at $t\rightarrow\infty$) probability to find the particle at the point it was located at $t = 0$ (Andeson criterion). Definition of the localization length is introduced. The computer experiments confirming correctness of the calculations are described.
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