非中心情形下二维空间的束缚态
Bound states in two spatial dimensions in the non-central case
摘要：
我们推导出一个约束上的负能量束缚态的总数在两个空间维度的潜在的Schwinger方法的适应推导出Birman-Schwinger约束在三维空间。具体地说，用计算零能束缚态存在的g_i的个数代替计算g=1时势gV中束缚态的个数，从而使零能波函数积分方程的核对称化.求解的关键之一是用齐次积分方程代替非齐次积分方程。
英文摘要：
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.
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