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Matematicheskie Zametki, 2016, Volume 99, Issue 6, paper published in the English version journal (Mi mzm11230)  
This article is cited in 3 scientific papers (total in 3 papers)

Papers published in the English version of the journal

On the Crystal Ground State in the Schrödinger–Poisson Model with Point Ions

A. I. Komechab

a Faculty of Mathematics, Vienna University, Vienna, Austria
b Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
Citations (3)
Abstract: A space-periodic ground state is shown to exist for lattices of point ions in $\mathbb{R}^3$ coupled to the Schrödinger and scalar fields. The coupling requires renormalization due to the singularity of the Coulomb self-action. The ground state is constructed by minimizing the renormalized energy per cell. This energy is bounded from below when the charge of each ion is positive. The elementary cell is necessarily neutral.
Keywords: crystal, lattice, ion, charge, wave function, potential, Schrödinger equation, Poisson equation, renormalized energy, elementary cell, energy per cell, Coulomb energy, minimization, neutrality condition, spectrum, embedding theorems, Fourier transform, infrared divergence, variation.
Funding agency Grant number
Russian Foundation for Basic Research 14-50-00150
Received: 03.12.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 6, Pages 886–894
DOI: https://doi.org/10.1134/S0001434616050278
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. I. Komech, “On the Crystal Ground State in the Schrödinger–Poisson Model with Point Ions”, Math. Notes, 99:6 (2016), 886–894
Citation in format AMSBIB
\Bibitem{Kom16}
\by A.~I.~Komech
\paper On the Crystal Ground State in the Schr\"odinger--Poisson Model with Point Ions
\jour Math. Notes
\yr 2016
\vol 99
\issue 6
\pages 886--894
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\crossref{https://doi.org/10.1134/S0001434616050278}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3519304}
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\elib{https://elibrary.ru/item.asp?id=26840126}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84977108886}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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