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TMF, 1997, Volume 113, Number 3, Pages 413–431 (Mi tmf1089)  

This article is cited in 8 scientific papers (total in 8 papers)

Spectral properties of Hamiltonians with magnetic field under fixation of pseudomomentum. I

S. A. Vugal'ter, G. M. Zhislin

Scientific Research Institute of Radio Physics

Abstract: It is established that the energy operator of an $n$-particle neutral system in a homogeneous magnetic field with a fixed pseudomomentum can be written as some operator in the space of relative motion. For this operator, the HVZ-theorem for the localization of the essential spectrum is proved, accounting for the permutational symmetry for any $n\geq 2$. For $n=2$, the conditions of finiteness and infinity of the discrete spectrum and spectral asymptotic behavior are found. The result can be applied, in particular, to the Hamiltonian of the hydrogen atom in the homogeneous magnetic field.

DOI: https://doi.org/10.4213/tmf1089

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English version:
Theoretical and Mathematical Physics, 1997, 113:3, 1543–1558

Bibliographic databases:

Received: 28.04.1997

Citation: S. A. Vugal'ter, G. M. Zhislin, “Spectral properties of Hamiltonians with magnetic field under fixation of pseudomomentum. I”, TMF, 113:3 (1997), 413–431; Theoret. and Math. Phys., 113:3 (1997), 1543–1558

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\pages 1543--1558
\crossref{https://doi.org/10.1007/BF02634514}
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. G. M. Zhislin, “Spectral properties of Hamiltonians with a magnetic field at a fixed pseudomomentum. III”, Theoret. and Math. Phys., 120:2 (1999), 1058–1073  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. S. A. Vugal'ter, G. M. Zhislin, “The Discrete Spectrum of the Hamiltonians of Atoms in a Homogeneous Magnetic Field”, Funct. Anal. Appl., 34:1 (2000), 64–66  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Zhislin, GM, “The spectral properties of the Hamiltonians of charged systems in a homogeneous magnetic field”, Doklady Mathematics, 63:2 (2001), 185  mathscinet  zmath  isi
    5. 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  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. G. M. Zhislin, “Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: II. The Structure of the Pure Point Spectrum”, Theoret. and Math. Phys., 134:2 (2003), 240–253  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Vugalter, S, “Bound states of atoms in a homogeneous magnetic field”, Mathematische Nachrichten, 278:7–8 (2005), 918  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    8. Last, Y, “The essential spectrum of Schrodinger, Jacobi, and CMV operators”, Journal D Analyse Mathematique, 98 (2006), 183  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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