标题： 量子格林函数的普遍行为 显示英文标题

标题： Universal behavior of quantum Green's functions

摘要： 我们考虑一个一般的单粒子哈密顿量 H = -\Delta _r + u(r)，它定义在一个d维的区域中。 感兴趣的对象是时间无关的格林函数 G_z(r,r') = < r | (z-H)^{-1} | r' >。 最近，在一维（1D）情况下，格林函数问题以逆形式被明确求解，其中格林函数的对角元素作为规定变量。 本文的第一个目的是从一维逆解中提取关于格林函数的信息，这些信息不能直接从其定义中得出。 其中，这些信息包括格林函数在区域边界附近的普遍行为，即与u(r)无关的行为。 第二个目的是将逆形式推广到更高维度，特别是三维（3D），并推导出各种约束区域边界形状下格林函数的普遍形式。 显示英文摘要

摘要： We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined in a d-dimensional domain. The object of interest is the time-independent Green function G_z(r,r') = < r | (z-H)^{-1} | r' >. Recently, in one dimension (1D), the Green's function problem was solved explicitly in inverse form, with diagonal elements of Green's function as prescribed variables. The first aim of this paper is to extract from the 1D inverse solution such information about Green's function which cannot be deduced directly from its definition. Among others, this information involves universal, i.e. u(r)-independent, behavior of Green's function close to the domain boundary. The second aim is to extend the inverse formalism to higher dimensions, especially to 3D, and to derive the universal form of Green's function for various shapes of the confining domain boundary.