%0 Journal Article
%T Upper and lower bounds for an eigenvalue associated with a positive eigenvector
%A Amaury Mouchet
%J Mathematics
%D 2005
%I arXiv
%R 10.1063/1.2168124
%X When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like inequalities and can be applied to non-necessarily purely quadratic Hamiltonians. An application for a magnetic Hamiltonian is given and the case of a discrete Schrodinger operator is also discussed. It is shown how this approach leads to some explicit bounds on the ground-state energy of a system made of an arbitrary number of attractive Coulombian particles.
%U http://arxiv.org/abs/math/0505541v1