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 TMF, 1999, Volume 120, Number 2, Pages 291–308 (Mi tmf776)

Spectral properties of Hamiltonians with a magnetic field at a fixed pseudomomentum. III

G. M. Zhislin

Scientific Research Institute of Radio Physics

Abstract: The general results (see previous Part II) on the structure of the discrete spectra of energy operators of neutral systems in a homogeneous magnetic field at a fixed pseudomomentum are proved to be applicable to Hamiltonians of arbitrary atoms. Asymptotic expressions for the discrete spectra of Hamiltonians in the presence of a homogeneous magnetic field are found for arbitrary atoms. This paper completes the investigation of the spectral properties of Hamiltonians of neutral systems in a homogeneous magnetic field at a fixed pseudomomentum. The essential and discrete parts of the spectrum for such systems were found previously; however, whether the theorems in Part II were valid for actual $n$-particle systems remained an open question for the case $n>3$.

DOI: https://doi.org/10.4213/tmf776

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English version:
Theoretical and Mathematical Physics, 1999, 120:2, 1058–1073

Bibliographic databases:

Citation: G. M. Zhislin, “Spectral properties of Hamiltonians with a magnetic field at a fixed pseudomomentum. III”, TMF, 120:2 (1999), 291–308; Theoret. and Math. Phys., 120:2 (1999), 1058–1073

Citation in format AMSBIB
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\by G.~M.~Zhislin
\paper Spectral properties of Hamiltonians with a magnetic field at a fixed pseudomomentum.~III
\jour TMF
\yr 1999
\vol 120
\issue 2
\pages 291--308
\mathnet{http://mi.mathnet.ru/tmf776}
\crossref{https://doi.org/10.4213/tmf776}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1737293}
\zmath{https://zbmath.org/?q=an:1086.81512}
\elib{https://elibrary.ru/item.asp?id=13318963}
\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 120
\issue 2
\pages 1058--1073
\crossref{https://doi.org/10.1007/BF02557412}

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This publication is cited in the following articles:
1. Zhislin, GM, “The spectral properties of the Hamiltonians of charged systems in a homogeneous magnetic field”, Doklady Mathematics, 63:2 (2001), 185
2. G. M. Zhislin, “Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: I. General Characteristic of the Spectrum”, Theoret. and Math. Phys., 133:1 (2002), 1390–1405
3. Vugalter, S, “Bound states of atoms in a homogeneous magnetic field”, Mathematische Nachrichten, 278:7–8 (2005), 918
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