Hooke's law correlation in two-electron systems

Abstract

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 ${}^{1}S$ 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 Schrödinger 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.

7 pages, 5 figures

References in corpus (3)

• Two electrons on a hypersphere: a quasi-exactly solvable model
• Ground state of two electrons on a sphere
• Correlation energy of two electrons in the high-density limit

Cited by in corpus (4)

• Excited states of spherium
• A Tale of Two Electrons: Correlation at High Density
• Correlation energy of two electrons in a ball
• Ground state of two electrons on concentric spheres