Virial theorem for variational functions in collision theory

Publisher Website
Google Scholar
Abstract
It is proved that if a scaling parameter alpha contained in a trial function uT is optimised using Kohn's variational principle, then the virial theorem is satisfied by the optimized variational function and the variationally determined phase shift, provided that the asymptotic form of uT does not depend upon alpha . By considering the cases of the scattering of electrons by the static potential of atomic hydrogen, and the scattering of particles by screened Coulomb potentials, it is shown that the virial theorem provides a valuable method for determining the optimum value of the scaling parameter and estimating the accuracy of the variationally determined trial function.