On a New Treatment of Some Eigenvalue Problems
On a New Treatment of Some Eigenvalue Problems
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一些特征值问题的新处理
DOI：
10.1103/physrev.59.737
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发表时间：
1941
期刊：
影响因子：
--
通讯作者：
L. Infeld
中科院分区：
文献类型：
--
作者：
L. Infeld
提出了一种处理量子力学中最重要的本征值问题的新方法。用线性算子对方程进行因式分解后，就可以立即找到解。这些作用于归一化特征函数的算子将其转化为新的归一化特征函数，一旦知道基本特征函数，就可以找到所有的解。这个基本特征函数是一个简单的一阶微分方程式的解。在一个特例中更充分地解释了基本理论(第1节)，然后明确地制定了程序规则(第2节)。论文的其余部分包括应用，包括根据狄拉克理论处理的开普勒问题。
A new method for treating the most important eigenvalue problems in quantum mechanics is developed. The solutions can be found immediately once the equations are factorized by means of linear operators. These operators acting on a normalized eigenfunction change it into a new normalized eigenfunction and all solutions can be found once the basic eigenfunction is known. This basic eigenfunction is a solution of a simple differential equation of the first order. The underlying theory is explained more fully on a special case (Section 1) and then the rules of procedure are formulated explicitly (Section 2). The rest of the paper contains applications including the Kepler problem treated according to Dirac's theory.