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 TMF, 1999, Volume 118, Number 1, Pages 15–39 (Mi tmf683)

Spectral properties of Hamiltonians with a magnetic field at a fixed pseudomoment. II

G. M. Zhislin

Scientific Research Institute of Radio Physics

Abstract: The discrete spectrum of multiparticle Hamiltonians $H_0$ of neutral systems in a homogeneous magnetic field is studied at a fixed pseudomoment. A general theorem is proved, which describes the discrete spectrum of $H_0$ under certain conditions in terms of constructed effective one-dimensional differential operators with a known spectrum structure. Based on this theorem, the conditions for a finite or infinite spectrum and the spectral asymptotic forms of the operator $H_0$ are obtained. The results can be applied to Hamiltonians of any atoms.

DOI: https://doi.org/10.4213/tmf683

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English version:
Theoretical and Mathematical Physics, 1999, 118:1, 12–31

Bibliographic databases:

Citation: G. M. Zhislin, “Spectral properties of Hamiltonians with a magnetic field at a fixed pseudomoment. II”, TMF, 118:1 (1999), 15–39; Theoret. and Math. Phys., 118:1 (1999), 12–31

Citation in format AMSBIB
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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 pseudomomentum. III”, Theoret. and Math. Phys., 120:2 (1999), 1058–1073
2. 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
3. Zhislin, GM, “The spectral properties of the Hamiltonians of charged systems in a homogeneous magnetic field”, Doklady Mathematics, 63:2 (2001), 185
4. 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
5. Vugalter, S, “Bound states of atoms in a homogeneous magnetic field”, Mathematische Nachrichten, 278:7–8 (2005), 918
6. Last, Y, “The essential spectrum of Schrodinger, Jacobi, and CMV operators”, Journal D Analyse Mathematique, 98 (2006), 183
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