S. A. Vugal'ter, G. M. Zhislin, “Localization of the essential spectrum of the energy operators of <nobr>$n$</nobr>-particle quantum systems in a magnetic field”, TMF, 1993, Volume 97, Number 1,Pages <nobr>94

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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

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