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Holas, Howard and March [Phys. Lett. A {\bf 310}, 451 (2003)] have obtainedanalytic solutions for ground-state properties of a whole family oftwo-electron spin-compensated harmonically confined model atoms whose differentmembers are characterized by a specific interparticle potential energyu($r_{12}$). Here, we make a start on the dynamic generalization of theharmonic external potential, the motivation being the serious criticismlevelled recently against the foundations of time-dependent density-functionaltheory (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-dependentelectron density for arbitrary interparticle interaction, which is fullydetermined by an one-dimensional non-interacting Hamiltonian. Moreover, aclosed solution for the momentum space density in the Moshinsky model isobtained.

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