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 (6)

• Density functional theory for strongly interacting electrons
• Two electrons on a hypersphere: a quasi-exactly solvable model
• Ground state of two electrons on a sphere
• Study of the discontinuity of the exchange-correlation potential in an exactly soluble case
• Correlation energy of two electrons in the high-density limit
• Adiabatic connection at negative coupling strengths

Cited by in corpus (15)

• Exact wave functions of two-electron quantum rings
• Excited states of spherium
• Uniform electron gases. I. Electrons on a ring
• Uniform electron gases
• Thinking outside the box: the uniform electron gas on a hypersphere
• 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
• The lowest excited configuration of harmonium
• Two-electron atom with a screened interaction
• Harmonium as a laboratory for mathematical chemistry
• Testing one-body density functionals on a solvable model
• Correlation energy of anisotropic quantum dots
• Harmonically trapped jellium
• Distribution of $r_{12}\cdot p_{12}$ in quantum systems