Original scientific paper
High energy asymptotics for eigenvalues of the Schrödinger operator with a matrix potential
Didem Co\d{s}kan
; Department of Mathematics, Faculty of Science, Dokuz Eylül University, Izmir, Turkey
Sedef Karakiliç
; Department of Mathematics, Faculty of Science, Dokuz Eylül University, Izmir, Turkey
Abstract
We consider a Schr\"{o}dinger operator with a matrix potential defined in $L_{2}^{m}(Q)$ by the differential expression $Lu= - \Delta u + Vu$ and the Neumann boundary condition, where $Q$ is a $d$-dimensional parallelepiped and $V$ a matrix potential, $d\geq 2$, $m\geq 2$.
We obtain the high energy asymptotics of arbitrary order for
a rich set of eigenvalues.
Keywords
Schrödinger operator; Neumann condition; perturbation; matrix potential
Hrčak ID:
74900
URI
Publication date:
21.12.2011.
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