Bound states in two spatial dimensions in the non-central case
数学物理
2015-06-26 v1 math.MP
摘要
We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting the number of bound states in a potential gV for g=1 is replaced by counting the number of g_i's for which zero energy bound states exist, and then the kernel of the integral equation for the zero-energy wave functon is symmetrized. One of the keys of the solution is the replacement of an inhomogeneous integral equation by a homogeneous integral equation.
引用
@article{arxiv.math-ph/0310035,
title = {Bound states in two spatial dimensions in the non-central case},
author = {Andre Martin and Tai Tsun Wu},
journal= {arXiv preprint arXiv:math-ph/0310035},
year = {2015}
}
备注
Work supported in part by the U.S. Department of Energy under Grant No. DE-FG02-84-ER40158