On the existence of effective potentials in time-dependent density functional theory

TL;DR

This paper explores the conditions under which effective potentials exist in time-dependent density functional theory, providing proofs and characterizations of v-representable densities and their independence from interactions.

Contribution

It establishes the existence conditions for effective potentials and characterizes v-representable densities in time-dependent density functional theory.

Findings

Existence of effective potentials under certain restrictions.

V-representable densities are independent of interactions.

Conditions for solutions of Sturm-Liouville problems are outlined.

Abstract

We investigate the existence and properties of effective potentials in time-dependent density functional theory. We outline conditions for a general solution of the corresponding Sturm-Liouville boundary value problems. We define the set of potentials and v-representable densities, give a proof of existence of the effective potentials under certain restrictions, and show the set of v-representable densities to be independent of the interaction.