# Solver for the electronic V-representation problem of time-dependent density functional theory

## TL;DR

This paper introduces a new solver for the scalar time-dependent Kohn-Sham potential in TDDFT, providing numerical results and insights into $V$-representability, with potential for improved quantum system simulations.

## Contribution

The paper presents a novel solver for the time-dependent Kohn-Sham potential and offers a new characterization of $V$-representability for one-electron systems.

## Key findings

- Successful numerical implementation for one- and two-electron systems
- New insights into $V$-representability conditions
- Potential pathways for improved quantum dynamics simulations

## Abstract

One route to numerically propagating quantum systems is time-dependent density functional theory (TDDFT). The application of TDDFT to a particular system's time evolution is predicated on $V$-representability which we have analyzed in a previous publication. Here we describe a newly developed solver for the scalar time-dependent Kohn-Sham potential. We present and interpret the force-balance equation central to our numerical method, describe details of its implementation, and present illustrative numerical results for one- and two-electron systems. A new characterization of $V$-representability for one-electron systems is also included along with possible improvements and future directions.