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

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://sro.sussex.ac.uk/id/eprint/46391
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