Melgaard, Michael (2002) On bound states for systems of weakly coupled Schrödinger equations in one space dimension. Journal of Mathematical Physics, 43 (11). pp. 5365-5385. ISSN 0022-2488

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Abstract

We establish the Birman–Schwinger relation for a class of Schrödinger operators −d2/dx2⊗1H+V on L2(math,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 Schrödinger 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

Item Type:	Article
Keywords:	eigenvalues and eigenfunctions; bound states; quantum theory; Schrödinger equation
Schools and Departments:	School of Mathematical and Physical Sciences > Mathematics
Subjects:	Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User:	Michael Melgaard
Date Deposited:	19 Sep 2013 13:24
Last Modified:	19 Sep 2013 13:24
URI:	http://srodev.sussex.ac.uk/id/eprint/46391

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