### Abstract

A third-order linear homogeneous differential equation is first derived for the local density of s-states only, N_{s}(r, E), for a general central potential V(r). The major example presented is then for the bare Coulomb potential -Ze^{2}/r, for which analytical forms are obtained for both N_{s}(r, E) and for the total density of states N(r, E). In the appendix, the repulsive linear potential case is also solved analytically.

Original language | English |
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Pages (from-to) | 6473-6481 |

Number of pages | 9 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 36 |

Issue number | 23 |

DOIs | |

Publication status | Published - Jun 13 2003 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*36*(23), 6473-6481. https://doi.org/10.1088/0305-4470/36/23/312

**Local density of states N(r, E) for central fields, with energy E in the continuum : Especially the coulomb potential.** / Howard, I. A.; March, N. H.; Nagy, A.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 36, no. 23, pp. 6473-6481. https://doi.org/10.1088/0305-4470/36/23/312

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TY - JOUR

T1 - Local density of states N(r, E) for central fields, with energy E in the continuum

T2 - Especially the coulomb potential

AU - Howard, I. A.

AU - March, N. H.

AU - Nagy, A.

PY - 2003/6/13

Y1 - 2003/6/13

N2 - A third-order linear homogeneous differential equation is first derived for the local density of s-states only, Ns(r, E), for a general central potential V(r). The major example presented is then for the bare Coulomb potential -Ze2/r, for which analytical forms are obtained for both Ns(r, E) and for the total density of states N(r, E). In the appendix, the repulsive linear potential case is also solved analytically.

AB - A third-order linear homogeneous differential equation is first derived for the local density of s-states only, Ns(r, E), for a general central potential V(r). The major example presented is then for the bare Coulomb potential -Ze2/r, for which analytical forms are obtained for both Ns(r, E) and for the total density of states N(r, E). In the appendix, the repulsive linear potential case is also solved analytically.

UR - http://www.scopus.com/inward/record.url?scp=0037757800&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037757800&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/23/312

DO - 10.1088/0305-4470/36/23/312

M3 - Article

VL - 36

SP - 6473

EP - 6481

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 23

ER -