### Abstract

Holas and March (1995) established a force-balance equation from the many-electron Schrödinger equation. Here, we propose this as a basis for the construction of a (usually approximate) differential equation for the ground-state electron density. By way of example we present the simple case of two-electron systems with different external potentials but with weak electron-electron Coulomb repulsion λe^{2}/r_{12}. In this case first-order Rayleigh-Schrödinger (RS) perturbation theory of the ground-state wave function is known to lead to a compact expression for the first-order density matrix γ(r,r′) in terms of its diagonal density ρ(r) and the density corresponding to λ = 0. This result allows the force-balance equation to be written as a third-order linear, differential homogeneous equation for the ground-state electron density ρ(r). The example of the two-electron Hookean atom is treated: For this case one can also transcend the first-order RS perturbation theory and get exact results for discrete choices of force constants (external potential).

Original language | English |
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Pages (from-to) | 716-720 |

Number of pages | 5 |

Journal | International Journal of Quantum Chemistry |

Volume | 77 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 15 2000 |

### Keywords

- Ground-state electron density
- Rayleigh-Schrödinger perturbation theory
- Virial theorem

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Physical and Theoretical Chemistry

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## Cite this

*International Journal of Quantum Chemistry*,

*77*(4), 716-720. https://doi.org/10.1002/(SICI)1097-461X(2000)77:4<716::AID-QUA4>3.0.CO;2-C