Operator interpretation of resonances arising in spectral problems for 2x2 matrix Hamiltonians

1998/09/30 by A. K. Motovilov, R. Mennicken
Physics and Astronomy · Mathematics · #math-ph #hep-ph #math.MP #nucl-th #msc:47A56 #msc:47Nxx #msc:47N50 #msc:47A40

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published as Operator Theory: Advances and Applications, Vol. 108 (1999), pp. 315-322 · LaTeX, 8 pages, no figures; Contribution to Proceedings of the Conference ``Mathematical Results in Quantum Mechanics (QMath7)'', Prague, June 22-26, 1998. Published version of the paper

arxiv created 1999/06/10 · arxiv updated 2009/11/30

Abstract

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer function which reproduce certain parts of its spectrum including resonances situated in the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis properties for the root vectors of the transfer function (including those for the resonances) are proved.

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