量子力学哈密顿量的显式格林算符。I.氢原子
Explicit Green operators for quantum mechanical Hamiltonians. I. The hydrogen atom
摘要：
研究了一种新的方法来确定量子多粒子系统在通过奇异库仑势相互作用的粒子的聚并点附近的渐近行为。这个问题是电子结构理论中的一个基本问题，它可以为数值模拟建立准确有效的模型。在我们的方法中，粒子的聚结点被视为嵌入在电子的配置空间中的几何奇点。基于一般的奇异伪微分学，我们给出了一个计算非相对论性哈密顿量的参量和相应格林算符的递推格式。在我们的奇异演算中，格林算子编码了本征函数的所有渐近信息。给出了氢原子和等电子离子的格林算符的显式计算和渐近表示。
英文摘要：
We study a new approach to determine the asymptotic behaviour of quantum many-particle systems near coalescence points of particles which interact via singular Coulomb potentials. This problem is of fundamental interest in electronic structure theory in order to establish accurate and efficient models for numerical simulations. Within our approach, coalescence points of particles are treated as embedded geometric singularities in the configuration space of electrons. Based on a general singular pseudo-differential calculus, we provide a recursive scheme for the calculation of the parametrix and corresponding Green operator of a nonrelativistic Hamiltonian. In our singular calculus, the Green operator encodes all the asymptotic information of the eigenfunctions. Explicit calculations and an asymptotic representation for the Green operator of the hydrogen atom and isoelectronic ions are presented.
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