On the Theory of the Hydrogen Atom
On the Theory of the Hydrogen Atom
复制标题
DOI：
10.1142/9789814542319_0009
复制
发表时间：
1988-12
期刊：
影响因子：
--
通讯作者：
V. Fock
中科院分区：
文献类型：
--
作者：
V. Fock
动量空间中氢原子的Schrödinger方程与四维势理论中球谐的积分方程是相同的。氢方程的变换群因此是四维旋转群。这就解释了氢能级相对于方位量子数的简并性。从Schrödinger方程的潜在理论解释中得出的关系允许许多物理应用。该方法允许人们对康普顿效应理论中出现的束缚电子和类似问题的无限求和进行计算。使用简化的原子模型，可以进一步得到动量空间中密度矩阵、原子形状因子、筛选势等的显式表达式。
The Schrödinger equation for the hydrogen atom in momentum space is identical to the integral equation for the spherical harmonics of four-dimensional potential theory. The group of transformations for the hydrogen equation is therefore the four-dimensional rotation group. This explains the degeneracy of the hydrogen levels with regard to the azimuthal quantum numberl. The relations which follow from the potential theoretical interpretation of the Schrödinger equation permit numerous physical applications. The method allows one to evaluate the infinite sums which occur in the theory of the Compton effect for bound electrons and similar problems. Using a simplified atomic model one can further obtain explicit expressions for the density matrix in momentum space, for atomic form factors, for the screening potential, etc…