2009/09/07 by Hellmut Baumgärtel, Baumgärtel, Hellmut
Mathematics · Physics and Astronomy · #47A40 #47D06 #81U20 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.0909.1174
openalex publication_date 2009/09/07 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28
For selected classes of quantum mechanical Hamiltonians a canonical\nassociation of a decay semigroup is presented. The spectrum of the generator of\nthis semigroup is a pure eigenvalue spectrum and it coincides with the set of\nall resonances. The essential condition for the results is the meromorphic\ncontinuability of the scattering matrix onto \ℂ\∖(-\∞,0] and\nthe rims \ℝ-\± i0. Further finite multiplicity is assumed. The\napproach is based on an adaption of the Lax-Phillips scattering theory to\nsemi-bounded Hamiltonians. It is applied to trace class perturbations with\nanalyticity conditions. A further example is the potential scattering for\ncentral-symmetric potentials with compact support and angular momentum 0.\n