High energy asymptotics for eigenvalues of the Schrodinger operator with a matrix potential

COŞKAN ÖZALP D., KARAKILIÇ S.

MATHEMATICAL COMMUNICATIONS, vol.16, no.2, pp.551-567, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 2011
  • Journal Name: MATHEMATICAL COMMUNICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.551-567
  • Keywords: Schrodinger operator, Neumann condition, perturbation, matrix potential, SPECTRUM, FORMULAS
  • Dokuz Eylül University Affiliated: Yes

Abstract

We consider a Schrodinger 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 >= 2, m >= 2. We obtain the high energy asymptotics of arbitrary order for a rich set of eigenvalues.