Dynamical generalization of a solvable family of two-electron model atoms with general interparticle repulsion

TL;DR

This paper extends a family of exactly solvable two-electron atoms to include dynamic external potentials, deriving a simplified density expression and a closed-form momentum space density for the Moshinsky model, addressing foundational issues in time-dependent density-functional theory.

Contribution

It introduces a dynamic generalization of a solvable two-electron model, providing explicit density expressions and addressing criticisms of time-dependent density-functional theory.

Findings

Derived a simplified expression for time-dependent electron density.

Obtained a closed-form solution for momentum space density in the Moshinsky model.

Extended the family of solvable two-electron models to include dynamics.

Abstract

Holas, Howard and March [Phys. Lett. A {\bf 310}, 451 (2003)] have obtained analytic solutions for ground-state properties of a whole family of two-electron spin-compensated harmonically confined model atoms whose different members are characterized by a specific interparticle potential energy u($r_{12}$). Here, we make a start on the dynamic generalization of the harmonic external potential, the motivation being the serious criticism levelled recently against the foundations of time-dependent density-functional theory (e.g. [J. Schirmer and A. Dreuw, Phys. Rev. A {\bf 75}, 022513 (2007)]). In this context, we derive a simplified expression for the time-dependent electron density for arbitrary interparticle interaction, which is fully determined by an one-dimensional non-interacting Hamiltonian. Moreover, a closed solution for the momentum space density in the Moshinsky model is obtained.