### Abstract

The self-consistent Thomas-Fermi atom satisfying Poisson's equation in D dimensions has a functional derivative of the kinetic energy T with respect to the ground-state density n(r) proportional to n^{2/D}. But the Poisson equation relates n^{1-2/D} to "reduced" density derivatives n^{-3(d2n/dr2)}. Thus δT/δn can be written also, quite compactly, solely in terms of these derivatives. An analytic solution to the Thomas-Fermi equation in D dimensions can be presented as an expansion about the known analytic solution at D = 2.

Original language | English |
---|---|

Pages (from-to) | 411-413 |

Number of pages | 3 |

Journal | International Journal of Quantum Chemistry |

Volume | 65 |

Issue number | 5 |

Publication status | Published - 1 Dec 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*International Journal of Quantum Chemistry*,

*65*(5), 411-413.

**Kinetic energy functional derivative for the Thomas-Fermi atom in D dimensions.** / March, Norman H.; Kais, Sabre.

Research output: Contribution to journal › Article

*International Journal of Quantum Chemistry*, vol. 65, no. 5, pp. 411-413.

}

TY - JOUR

T1 - Kinetic energy functional derivative for the Thomas-Fermi atom in D dimensions

AU - March, Norman H.

AU - Kais, Sabre

PY - 1997/12/1

Y1 - 1997/12/1

N2 - The self-consistent Thomas-Fermi atom satisfying Poisson's equation in D dimensions has a functional derivative of the kinetic energy T with respect to the ground-state density n(r) proportional to n2/D. But the Poisson equation relates n1-2/D to "reduced" density derivatives n-3(d2n/dr2). Thus δT/δn can be written also, quite compactly, solely in terms of these derivatives. An analytic solution to the Thomas-Fermi equation in D dimensions can be presented as an expansion about the known analytic solution at D = 2.

AB - The self-consistent Thomas-Fermi atom satisfying Poisson's equation in D dimensions has a functional derivative of the kinetic energy T with respect to the ground-state density n(r) proportional to n2/D. But the Poisson equation relates n1-2/D to "reduced" density derivatives n-3(d2n/dr2). Thus δT/δn can be written also, quite compactly, solely in terms of these derivatives. An analytic solution to the Thomas-Fermi equation in D dimensions can be presented as an expansion about the known analytic solution at D = 2.

UR - http://www.scopus.com/inward/record.url?scp=5444263126&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5444263126&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:5444263126

VL - 65

SP - 411

EP - 413

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 5

ER -