One-dimensional Lieb-Oxford bounds

摘要

We investigate and prove Lieb-Oxford bounds in one dimension by studying convex potentials that approximate the ill-defined Coulomb potential. A Lieb-Oxford inequality establishes a bound of the indirect interaction energy for electrons in terms of the one-body particle density rho (psi) of a wave function psi. Our results include modified soft Coulomb potential and regularized Coulomb potential. For these potentials, we establish Lieb-Oxford-type bounds utilizing logarithmic expressions of the particle density. Furthermore, a previous conjectured form Ixc(psi)>= -C1 integral R rho psi (x)2dx is discussed for different convex potentials.