S-矩阵双极点的Jordan块和Gamow-Jordan本征函数
Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix
摘要：
共振的偶然简并引起散射矩阵中的双极点、Jost函数中的双零点和径向Schroedinger方程的广义Gamow-Jordan本征函数的长度为2的Jordan链。广义Gamow-Jordan本征函数是束缚和共振能量本征函数的展开式的基本元素，加上一个复波数的散射波函数的连续体。在这个双正交基中，任何作为哈密顿函数的正则函数的算子都由一个复矩阵表示，除了秩为2的Jordan块之外，该复矩阵是对角的。格林函数中出现双极点以及Gamow-Jordan广义本征函数的非指数时间演化与复能量表示中的Jordan块有关。
英文摘要：
An accidental degeneracy of resonances gives rise to a double pole in the scattering matrix, a double zero in the Jost function and a Jordan chain of length two of generalized Gamow-Jordan eigenfunctions of the radial Schroedinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in bound and resonant energy eigenfunctions plus a continuum of scattering wave functions of complex wave number. In this biorthonormal basis, any operator which is a regular function of the Hamiltonian is represented by a complex matrix which is diagonal except for a Jordan block of rank two. The occurrence of a double pole in the Green's function, as well as the non-exponential time evolution of the Gamow-Jordan generalized eigenfunctions are associated to the Jordan block in the complex energy representation.
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