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

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

2007-08-10

arxiv.org/abs/0708.1418v2

Physics

Quantum Physics

5 pages, submitted to J. Phys. A

Scientific paper

10.1088/1751-8113/41/8/085304

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.

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