This article is cited in 1 paper

Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: II. The Structure of the Pure Point Spectrum

G. M. Zhislin

Scientific Research Institute of Radio Physics

Abstract: 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.

Received: 18.01.2002

DOI: 10.4213/tmf157

 English version: Theoretical and Mathematical Physics, 2003, 134:2, 240–253

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