半直线上自伴矩阵Schroedinger算子的高能分析和Levinson定理
High-Energy analysis and Levinson's theorem for the selfadjoint matrix Schroedinger operator on the half line
摘要：
本文讨论了半直线上具有自伴矩阵势的Schroedinger方程，原点为一般自伴边界条件。当矩阵势可积时，建立了相关的Jost矩阵、Jost矩阵的逆矩阵和散射矩阵的高能渐近性。在附加的假设下，矩阵势有一个第一时刻，莱文森定理推导出，有关的散射矩阵的行列式的自变量的变化的绑定状态的数量。
英文摘要：
The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the general selfadjoint boundary condition at the origin. When the matrix potential is integrable, the high-energy asymptotics are established for the related Jost matrix, the inverse of the Jost matrix, and the scattering matrix. Under the additional assumption that the matrix potential has a first moment, Levinson's theorem is derived, relating the number of bound states to the change in the argument of the determinant of the scattering matrix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
