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Article Dans Une Revue Journal of Mathematical Physics Année : 2006

Upper and lower bounds for an eigenvalue associated with a positive eigenvector

Résumé

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.
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Dates et versions

hal-00004980 , version 1 (25-05-2005)

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Amaury Mouchet. Upper and lower bounds for an eigenvalue associated with a positive eigenvector. Journal of Mathematical Physics, 2006, 47, pp.022109. ⟨hal-00004980⟩
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