One-dimensional hypervirial theorems in density functional theory

Abstract

For a restricted class of operators hypervirial theorems are established involving wavefunctions ψ i for N fermions which move independently in a common external one-dimensional potential V( x). Using this class it is possible to perform the summation over states ψ i yielding exact relations between ground state density ϱ and kinetic energy density ϵ k and potential V( x). It is checked to what extent the Thomas-Fermi expressions for ϱ and ϵ k satisfy these relations.