Converging bounds for the eigenvalues of multiminima potentials in two-dimensional space


TAŞELİ H., Eid R.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, vol.29, no.21, pp.6967-6982, 1996 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 21
  • Publication Date: 1996
  • Doi Number: 10.1088/0305-4470/29/21/027
  • Journal Name: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.6967-6982

Abstract

The eigenvalue problem in L(2)(R(2)) of Schrodinger operators with a polynomial perturbation has been replaced by one corresponding to the system confined in a box Omega with impenetrable walls. It is shown that the Dirichlet and the von Neumann problems in L(2)(Omega) generate upper and lower bounds, respectively, to the eigenvalues of the unbounded system. To illustrate the method, rapidly converging two-sided bounds for the energy levels of two- and three-well oscillators are presented, using simple trigonometric basis functions.