Abstract
We consider the analytic continuation of the transfer function for a 2 x 2 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.
*Financial support of this work by the DFG, INTAS and RFBR is kindly acknowledged
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Motovilov, A.K., Mennicken, R. (1999). Operator Interpretation of Resonances Arising in Spectral Problems for 2 x 2 Matrix Hamiltonians. In: Dittrich, J., Exner, P., Tater, M. (eds) Mathematical Results in Quantum Mechanics. Operator Theory Advances and Applications, vol 108. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8745-8_30
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DOI: https://doi.org/10.1007/978-3-0348-8745-8_30
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9754-9
Online ISBN: 978-3-0348-8745-8
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