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Isaac Newton Institute for Mathematical Sciences

A balance of kinetic and potential energies in the semi-classical limit

Author: YAFAEV (University of Rennes)

Abstract

Consider a bound state of a quantum particle in a potential well $v(x)$. Suppose that the energy of a particle is higher than the minimum of the function $v(x)$. We show that in the semi-classical limit, as the Planck constant $h$ tends to zero, the ratio of kinetic and potential energies tends to a finite positive limit.