The inverse problem of time-dependent density functional theory on the torus

We prove that, for any given sufficiently regular one-particle density, there exists a unique external potential for which the solution to the many-body Schrödinger equation has this prescribed density. This implies in particular that one can exactly reproduce the time-dependent density of an interacting system using non-interacting electrons, which is at the heart of time-dependent density functional theory. Our result covers the Coulomb interaction and densities arising from extended nuclei.

Source: arXiv:2609.08984v1 - http://arxiv.org/abs/2609.08984v1 PDF: https://arxiv.org/pdf/2609.08984v1 Original Link: http://arxiv.org/abs/2609.08984v1