We consider the time-independent Green's function for the Schrödinger operator with a one-particle potential, defined in a d-dimensional domain. Recently, in one dimension (ID), the Green's function problem was solved explicitly in inverse form, with diagonal elements of the Green's function as prescribed variables. In this article, the ID inverse solution is used to derive leading behavior of the Green's function close to the domain boundary. The emphasis is put onto "universal" expansion terms which are dominated by the boundary and do not depend on the particular shape of the applied potential. The inverse formalism is extended to higher dimensions, especially to 3D, and subsequently the boundary form of the Green's function is predicted for an arbitrarily shaped domain boundary.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics