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

We study the pure point spectrum of the energy operator H(PΣ) 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 PΣ of the pseudomomentum components of the system. We prove that the discrete spectrum H(PΣ) 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.