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Prog. Theor. Phys. Vol. 109 No. 4 (2003) pp. 563-573
Direct Sum of Coulomb Potential without Ambiguities of Conditionally Convergent Series
Hiroki Takemoto,
Taisei Ohyama* and
Akihiro Tohsaki
Department of Fine Materials Engineering, Shinshu University, Ueda 386-8567,
Japan
(Received November 28, 2002)
Abstract:
We propose a definitive expression to evaluate electrostatic energies under
periodic conditions, starting from the Yukawa potential with a finite
range and summing up positive and negative contributions separately.
We find a dimension-dependent function that can be used to solve
problems concerning divergences and ambiguities in
the direct sum of Coulomb potentials. The infinite-range limit of this
function leads to a universal constant independent of lattice
structure, which reveals the origin of ambiguities from
conditionally convergent series in the sum of Coulomb potentials.
URL :
http://ptp.ipap.jp/link?PTP/109/563/
DOI : 10.1143/PTP.109.563
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Citing Article(s) :
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Progress of Theoretical Physics Vol. 111 No. 2 (2004) pp. 213-228
:
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Electrostatic Energy of an Aggregate of Point Charges with Periodicity in a Uniform Background
-
Hiroki Takemoto and Akihiro Tohsaki
-
Progress of Theoretical Physics Vol. 112 No. 3 (2004) pp. 489-497
:
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Dependence of the Electrostatic Energy on the Dimension of the Periodicity in a Uniform Background
-
Hiroki Takemoto and Akihiro Tohsaki
-
Progress of Theoretical Physics Vol. 113 No. 2 (2005) pp. 327-339
:
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Electrostatic Energies of Crystals in Space of Arbitrary Dimension
-
Hiroki Takemoto and Akihiro Tohsaki
