On bound states for systems of weakly coupled Schrodinger equations in one space dimension

摘要

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. [References: 33]