On bound states for systems of weakly coupled Schrodinger equations in one space dimension
2002 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 43, no 11, 5365-5385 p.Article in journal (Refereed) Published
We establish the Birman-Schwinger relation for a class of Schrodinger operators -d(2)/dx(2)circle times1(H)+V on L-2(R,H), where H is an auxiliary Hilbert space and V is an operator-valued potential. As an application we give an asymptotic formula for the bound states which may arise for a weakly coupled Schrodinger operator with a matrix potential (having one or more thresholds). In addition, for a two-channel system with eigenvalues embedded in the continuous spectrum we show that, under a small perturbation, such eigenvalues turn into resonances.(C) 2002 American Institute of Physics.
Place, publisher, year, edition, pages
2002. Vol. 43, no 11, 5365-5385 p.
IdentifiersURN: urn:nbn:se:uu:diva-174116DOI: 10.1063/1.1510175ISI: 000178767300009OAI: oai:DiVA.org:uu-174116DiVA: diva2:526504