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 $Lu=-\mathrm{\Delta }u+Vu$ and the Neumann boundary condition, where $Q$ is a $d$-dimensional parallelepiped and $V$ a matrix potential, $d\ge 2$, $m\ge 2$.
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

https://hrcak.srce.hr/74900

Publication date:

21.12.2011.

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