Year: 2010
Type: article
Abstract: We study the properties of the Hooke's law correlation energy (${E}_{\mathrm{c}}$), defined as the correlation energy when two electrons interact 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 that highlights the main differences of the ${E}_{\mathrm{c}}$ 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.
Source: Physical Review A
Author: Pierre-François Loos
Institution: Australian National University
Language: English
Topic: Atomic and Molecular Physics
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2122715436