Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: II.~The Structure of the Pure Point Spectrum
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 2, pp. 273-288
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We study the pure point spectrum of the energy operator $H(P_\Sigma)$ of a many-particle charged quantum system in a homogeneous magnetic field based on the results in our previous work under fixation of the sum $P_\Sigma$ of the pseudomomentum components of the system. We prove that the discrete spectrum $H(P_\Sigma)$ of a short-range system is infinite under some conditions (which, for example, hold for a system of two oppositely charged particles) even in the case of a finitely supported potential. For a long-range system of the type of a $(+)$-ion of an atom (including the ion), the discrete spectrum is infinite.
Keywords:
Hamiltonian, homogeneous magnetic field, spectral properties, relative motion, pseudomomentum.
@article{TMF_2003_134_2_a8,
author = {G. M. Zhislin},
title = {Spectral {Properties} of {Hamiltonians} of {Charged} {Systems} in a {Homogeneous} {Magnetic} {Field:} {II.~The} {Structure} of the {Pure} {Point} {Spectrum}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {273--288},
publisher = {mathdoc},
volume = {134},
number = {2},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a8/}
}
TY - JOUR AU - G. M. Zhislin TI - Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: II.~The Structure of the Pure Point Spectrum JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2003 SP - 273 EP - 288 VL - 134 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a8/ LA - ru ID - TMF_2003_134_2_a8 ER -
%0 Journal Article %A G. M. Zhislin %T Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: II.~The Structure of the Pure Point Spectrum %J Teoretičeskaâ i matematičeskaâ fizika %D 2003 %P 273-288 %V 134 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a8/ %G ru %F TMF_2003_134_2_a8
G. M. Zhislin. Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: II.~The Structure of the Pure Point Spectrum. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 2, pp. 273-288. http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a8/