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

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

2010-09-07

arxiv.org/abs/1009.1387v1

Mathematics

Spectral Theory

Scientific paper

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.

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