The effect of cusps in time-dependent quantum mechanics

TL;DR

This paper investigates how spatial cusps in initial wavefunctions cause non-analytic time behavior in quantum systems and proposes a method to accurately compute short-time dynamics while confirming the validity of density functional theory in these scenarios.

Contribution

It introduces a new approach for calculating short-time behavior in quantum systems with cusps and demonstrates the robustness of density functional theory despite non-analytic initial conditions.

Findings

Spatial cusps cause non-analytic time evolution.

The proposed method accurately captures short-time dynamics.

Density functional theory remains valid with time-analytic potentials.

Abstract

Spatial cusps in initial wavefunctions can lead to non-analytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor-expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time-analytic.