Eigenfunction expansions associated with the Schroedinger operators and their applications to scattering theory
Eigenfunction expansions associated with the Schroedinger operators and their applications to scattering theory
复制标题
与薛定谔算子相关的本征函数展开及其在散射理论中的应用
DOI：
10.1007/bf00252896
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发表时间：
1960
影响因子：
2.5
通讯作者：
Teruo Ikebe
中科院分区：
文献类型：
--
作者：
Teruo Ikebe
本文讨论与薛定谔算子A+ q (x)相关的特征函数展开式，其中~]表示三维拉普拉斯算子，q (z)是一个实值势函数，定义在整个三维欧几里德空间E= E s上，该空间在无穷远处趋于0。应用所得结果阐明薛定谔算符谱的一些性质，并说明在描述量子力学散射过程中起重要作用的s矩阵的酉性。
In the present paper we shall be concerner with eigenfunction expansions associated with the Schroedinger operator--A+ q (x), where~] denotes the3-dimensional Laplacian and q (z) is a real-valued potential function-defined on the whole 3-dimensional Euclidean space E= E s, which tends to 0 at infinity: Solving the expansion problem, we go fo. rward to apply the results obtained to clarify some properties of the spectrum of the Schroedinger operator and to show the unitary character of the S-matrix that plays an important part in describing the scattering process in quantum mechanics.