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

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$r₁₂$. 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. \[J. Schirmer and A. Dreuw, Phys. Rev. A {bf 75}, 022513 (2007\]). 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.