排斥哈密顿量的定态散射理论
Stationary scattering theory for repulsive Hamiltonians
摘要：
本文讨论排斥哈密顿量的定态散射理论。我们证明了驻波算子的存在性和完备性以及散射矩阵的么正性。此外，我们完全刻画了具有最小增长的广义本征函数的渐近行为的散射矩阵。在我们的论证中，辐射条件的极限预解式边界起着重要的作用。实际上，它被用来构造驻波算子。
英文摘要：
In the present paper we discuss stationary scattering theory for repulsive Hamiltonians. We show the existence and completeness of stationary wave operators and unitarity of the scattering matrix. Moreover we completely characterize asymptotic behaviors of generalized eigenfunctions with minimal growth in terms of the scattering matrix. In our argument the radiation condition bounds for limiting resolvents play major roles. In fact, it is used to construct the stationary wave operators.
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