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

Abstract

Holas, Howard and March (2003 Phys. Lett. A 310 451) 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(r12). 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., Schirmer and Dreuw 2007 Phys. Rev. A 75 022513). In this context, we derive a simplified expression for the time-dependent electron density for arbitrary interparticle interaction, which is fully determined by a one-dimensional non-interacting Hamiltonian. Moreover, a closed solution for the momentum space density in the Moshinsky model is obtained.