Hooke's law correlation in two-electron systems

Details Hooke's law correlation in two-electron systems Hooke's law correlation in two-electron systems

2010-02-17

arxiv.org/abs/1002.3396v2

Phys. Rev. A 81, 032510 (2010).

Physics

Condensed Matter

Other Condensed Matter

7 pages, 5 figures

Scientific paper

10.1103/PhysRevA.81.032510

We study the properties of the Hooke's law correlation energy ($\Ec$), defined as the correlation energy when two electrons interact {\em via} a harmonic potential in a $D$-dimensional space. More precisely, we investigate the $^1S$ ground state properties of two model systems: the Moshinsky atom (in which the electrons move in a quadratic potential) and the spherium model (in which they move on the surface of a sphere). A comparison with their Coulombic counterparts is made, which highlights the main differences of the $\Ec$ in both the weakly and strongly correlated limits. Moreover, we show that the Schr\"odinger equation of the spherium model is exactly solvable for two values of the dimension ($D = 1 \text{and} 3$), and that the exact wave function is based on Mathieu functions.

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