2004/07/26 by Hellmut Baumgaertel, Baumgaertel, Hellmut
Mathematics · Physics and Astronomy · #46N50 #47A40 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:46N50 #msc:47A40
paper · pdf · doi:10.48550/arxiv.math-ph/0407059
23pages
arxiv created 2004/10/13 · arxiv updated 2009/12/01
Results from the Lax-Phillips Scattering Theory are used to analyze quantum mechanical scattering systems, in particular to obtain spectral properties of their resonances which are defined to be the poles of the scattering matrix. For this approach the interplay between the positive energy projection and the Hardy-space projections is decisive. Among other things it turns out that the spectral properties of these poles can be described by the (discrete) eigenvalue spectrum of a so-called truncated evolution, whose eigenvectors can be considered as the Gamov vectors corresponding to these poles. Further an expansion theorem of the positive Hardy-space part of vectors Sg (S scattering operator) into a series of Gamov vectors is presented.