### Abstract

After a brief survey on the application of the Thomas-Fermi statistical method to bare Coulomb potential satisfying Laplace equation in D dimensions, which then relates energy and chemical potential, we next focus attention on model atomic ions with merely one and two electrons in D dimensions. In particular, for a bare Coulomb field we use the nodeless radial eigenfunctions given by Herschbach in D dimensions to derive the spatial generalization of Kato's nuclear cusp theorem in D dimensions for D > 1. The unbinding of H ^{-} as a function of dimensionality D is also briefly referred.

Original language | English |
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Pages (from-to) | 266-270 |

Number of pages | 5 |

Journal | Physics and Chemistry of Liquids |

Volume | 50 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 2012 |

### Fingerprint

### Keywords

- cusp condition in bare Coulomb field
- electron liquid in D dimension
- generalization of Kato's theorem

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Materials Chemistry
- Condensed Matter Physics
- Physical and Theoretical Chemistry

### Cite this

**Some model inhomogeneous electron liquid in D dimensions : Relation between energy and chemical potential and a spatial generalisation of Kato's nuclear cusp theorem.** / March, N. H.; Nagy, A.

Research output: Contribution to journal › Article

*Physics and Chemistry of Liquids*, vol. 50, no. 2, pp. 266-270. https://doi.org/10.1080/00319104.2011.587191

}

TY - JOUR

T1 - Some model inhomogeneous electron liquid in D dimensions

T2 - Relation between energy and chemical potential and a spatial generalisation of Kato's nuclear cusp theorem

AU - March, N. H.

AU - Nagy, A.

PY - 2012/3

Y1 - 2012/3

N2 - After a brief survey on the application of the Thomas-Fermi statistical method to bare Coulomb potential satisfying Laplace equation in D dimensions, which then relates energy and chemical potential, we next focus attention on model atomic ions with merely one and two electrons in D dimensions. In particular, for a bare Coulomb field we use the nodeless radial eigenfunctions given by Herschbach in D dimensions to derive the spatial generalization of Kato's nuclear cusp theorem in D dimensions for D > 1. The unbinding of H - as a function of dimensionality D is also briefly referred.

AB - After a brief survey on the application of the Thomas-Fermi statistical method to bare Coulomb potential satisfying Laplace equation in D dimensions, which then relates energy and chemical potential, we next focus attention on model atomic ions with merely one and two electrons in D dimensions. In particular, for a bare Coulomb field we use the nodeless radial eigenfunctions given by Herschbach in D dimensions to derive the spatial generalization of Kato's nuclear cusp theorem in D dimensions for D > 1. The unbinding of H - as a function of dimensionality D is also briefly referred.

KW - cusp condition in bare Coulomb field

KW - electron liquid in D dimension

KW - generalization of Kato's theorem

UR - http://www.scopus.com/inward/record.url?scp=84859170627&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859170627&partnerID=8YFLogxK

U2 - 10.1080/00319104.2011.587191

DO - 10.1080/00319104.2011.587191

M3 - Article

AN - SCOPUS:84859170627

VL - 50

SP - 266

EP - 270

JO - Physics and Chemistry of Liquids

JF - Physics and Chemistry of Liquids

SN - 0031-9104

IS - 2

ER -