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.
@article{0505541,
author = {Mouchet, Amaury},
title = {Upper and lower bounds for an eigenvalue associated with a positive
eigenvector},
journal = {arXiv},
volume = {2005},
number = {0},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/0505541}
}
Mouchet, Amaury. Upper and lower bounds for an eigenvalue associated with a positive
eigenvector. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0505541/