( 18 ) The eigenvalue problem for ordinary differential equations of the second order and Heisenberg's theory of S-matrices
( 18 ) The eigenvalue problem for ordinary differential equations of the second order and Heisenberg's theory of S-matrices
复制标题
( 18 ) 二阶常微分方程的特征值问题和海森堡S矩阵理论
DOI：
10.1515/9781400869855-019
复制
发表时间：
1949
影响因子：
1.7
通讯作者：
K. Kodaira
中科院分区：
文献类型：
--
作者：
K. Kodaira
最近，E.C.Titchmarsh用一种新的方法处理了用二阶微分算子的本征函数表示的任意函数的展开式理论，并得到了有重要应用价值的结果。Titchmarsh方法完全基于留数演算。本文首先根据Hilbert空间中线性算子的一般理论，给出了Titchmarsh结果的另一种证明，然后将其应用于薛定谔方程，证明了关于S矩阵的一个Leisenberg2定理是成立的。
Recently E. C. Titchmarsh has treated the theory of expansion of arbitrary functions in terms of the eigenfunctions of a differential operator of the second order by a new method and obtained results of importance for applications.' The method of Titchmarsh is based solely on the calculus of residues. In the present paper we shall first give another proof of Titchmarsh's results based, on the general theory of linear operators in Hilbert space and, secondly, applying them to differential equations of Schrodinger type, show that a theorem of leisenberg2 concerning the S-matrix can be founded on these results.