Comments on the momentum density and the spatial form of the density-matrix of the Hooke's atom

TL;DR

This paper discusses the properties of the density-matrix and momentum density of the Hooke's atom, emphasizing the importance of the reciprocal form factor in understanding the off-diagonal elements of the reduced density-matrix.

Contribution

It provides insights into the reciprocal form factor of the Hooke's atom's density-matrix, building on previous work to better understand its off-diagonal structure.

Findings

Analysis of the integral form of the momentum density

Derivation of a closed-form expression for the reciprocal form factor

Enhanced understanding of the off-diagonal elements of the density-matrix

Abstract

In a recent paper, A. Akbari, N. H. March and A. Rubio [Phys. Rev. A. 76, 032510 (2007)] have investigated the one-electron reduced density-matrix and the momentum density of several two-electron model atoms, including the Hooke's atom. The method used by the authors for deriving an integral form of the momentum density is well suited for deriving a closed-form expression of the exact reciprocal form factor, which function is of importance inasmuch as it reflects the off-diagonal side of the exact reduced density-matrix.