量子力学散射系统共振态的衰变半群
Decay Semigroups for the Resonances of Quantum Mechanical Scattering Systems
摘要：
对于选定的量子力学哈密顿量类的衰变半群的一个典型的关联。这个半群的生成元的谱是一个纯本征值谱，它与所有共振点的集合一致。该结果的必要条件是散射矩阵在$\Bbb{C}\setminus(-\infty,0]$和边缘$\Bbb{R}_{-}\pm i0$上的亚纯连续性。进一步假设有限多重性。该方法是基于适应的Lax-Phillips散射理论的半有界哈密顿。它适用于迹类扰动与解析条件。另一个例子是具有紧支撑和角动量为0的中心对称势的势散射。
英文摘要：
For selected classes of quantum mechanical Hamiltonians a canonical association of a decay semigroup is presented. The spectrum of the generator of this semigroup is a pure eigenvalue spectrum and it coincides with the set of all resonances. The essential condition for the results is the meromorphic continuability of the scattering matrix onto $\Bbb{C}\setminus(-\infty,0]$ and the rims $\Bbb{R}_{-}\pm i0$. Further finite multiplicity is assumed. The approach is based on an adaption of the Lax-Phillips scattering theory to semi-bounded Hamiltonians. It is applied to trace class perturbations with analyticity conditions. A further example is the potential scattering for central-symmetric potentials with compact support and angular momentum 0.
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