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

D. R. Yafaev

doi:10.1088/1751-8113/43/47/474032

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arXiv · 1009.1387

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

D. R. Yafaev

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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.

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D. R. Yafaev. 2010-09-07. A generalized virial theorem and the balance of kinetic and potential energies in the semiclassical limit. https://doi.org/10.1088/1751-8113/43/47/474032

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