On the eigenvalues of a 3 by 3 non-Hermitian Hamiltonian

Ergun E., BAYRAM E.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.49, no.2, pp.609-617, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.1007/s10910-010-9767-2
  • Journal Name: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.609-617
  • Keywords: Discrete system, Non-Hermiticity, Jacobi matrix, Eigenvalue
  • Ankara University Affiliated: Yes

Abstract

In this paper, we are concerned with a 3 x 3 complex matrix Jacobi (tri-diagonal matrix) arised from a non-Hermitian discrete quantum system. Necessary and sufficient conditions for reality of the eigenvalues of the matrix in question are established.