S. A. Vugal'ter, G. M. Zhislin, “Localization of the essential spectrum of the energy operators of $n$-particle quantum systems in a magnetic field”, TMF, 97:1 (1993), 94–112; Theoret. and Math. Phys., 97:1 (1993), 1171

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Teoreticheskaya i Matematicheskaya Fizika, 1993, Volume 97, Number 1, Pages 94–112 (Mi tmf1726)

This article is cited in 7 scientific papers (total in 7 papers)

Localization of the essential spectrum of the energy operators of

$n$ -particle quantum systems in a magnetic field

S. A. Vugal'ter^a, G. M. Zhislin^b

^a Scientific-Research Physicotechnical Institute at the Nizhnii Novgorod State University
^b Scientific Research Institute of Radio Physics

Full-text PDF (1685 kB) Citations (7)

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Abstract: Theorems on the localization of the essential spectrum of given

$SO(2)$ symmetry for

$n$ -particle Hamiltonians in an external magnetic field are proved. The energy operators are studied for systems of arbitrary particles in the absence of an external potential field and for systems of identical particles in an external potential field. Some of the results were announced in earlier papers [1, 2].

Received: 11.08.1992

English version:
Theoretical and Mathematical Physics, 1993, Volume 97, Issue 1, Pages 1171–1185
DOI: https://doi.org/10.1007/BF01014810

Bibliographic databases:

Language: Russian

Citation: S. A. Vugal'ter, G. M. Zhislin, “Localization of the essential spectrum of the energy operators of

$n$ -particle quantum systems in a magnetic field”, TMF, 97:1 (1993), 94–112; Theoret. and Math. Phys., 97:1 (1993), 1171–1185

Citation in format AMSBIB

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\transl

\jour Theoret. and Math. Phys.

\yr 1993

\vol 97

\issue 1

\pages 1171--1185

\crossref{https://doi.org/10.1007/BF01014810}

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Linking options:

https://www.mathnet.ru/eng/tmf1726

https://www.mathnet.ru/eng/tmf/v97/i1/p94

This publication is cited in the following 7 articles:

Last, Y, “The essential spectrum of Schrodinger, Jacobi, and CMV operators”, Journal D Analyse Mathematique, 98 (2006), 183
Vugalter, S, “Bound states of atoms in a homogeneous magnetic field”, Mathematische Nachrichten, 278:7–8 (2005), 918
G. M. Zhislin, “Spectral properties of Hamiltonians with a magnetic field at a fixed pseudomoment. II”, Theoret. and Math. Phys., 118:1 (1999), 12–31
S. A. Vugal'ter, G. M. Zhislin, “Spectral properties of Hamiltonians with magnetic field under fixation of pseudomomentum. I”, Theoret. and Math. Phys., 113:3 (1997), 1543–1558
I. Laba, The IMA Volumes in Mathematics and its Applications, 89, Multiparticle Quantum Scattering With Applications to Nuclear, Atomic and Molecular Physics, 1997, 147
G. M. Zhislin, “Location of the essential spectrum of the energy operators of the quantum systems with nonincreasing magnetic field”, Theoret. and Math. Phys., 107:3 (1996), 720–732
S. A. Vugal'ter, G. M. Zhislin, “Stability of Systems of a Large Number of Particles in Magnetic Fields”, Funct. Anal. Appl., 30:2 (1996), 129–131

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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