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


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


The eigenvalue problem in L(2)(R(2)) of Schrodinger operators with a polynomial perturbation has been replaced by one corresponding to the system confined in a box Omega with impenetrable walls.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.