A generalized virial theorem and the balance of kinetic and potential energies in the semiclassical limit

Abstract

We obtain two-sided bounds on kinetic and potential energies of a bound state of a quantum particle in the semiclassical limit, as the Planck constant \hbar\ri 0. Proofs of these results rely on the generalized virial theorem obtained in the paper as well as on a decay of eigenfunctions in the classically forbidden region