S.A. Wugalter G.M. Zhislin
On the structure of the discrete spectrum of multiparticle hamiltonians with increasing magnetic fields
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

 35J10 Schrodinger operator, See also {35Pxx}

Abstract: The discrete spectrum of the hamiltonian H₀ of a manyparticle quantum system Z₁ in a magnetic field, which has the direction of z axis and infinitely increases at the infinity of (x,y)-plane, is studied in the spaces of the functions having arbitrary permutational symmetry. We consider the situation when the lower bound of the essential spectrum H₀ is determined only by the decompositions of Z₁ into two stable subsystems. For this case the description of the discrete spectrum H₀ is found in terms of the spectral properties of two effective one-dimensional two-particle operators without magnetic field. By using this we obtained the conditions of finiteness and infinity of the discrete spectrum H₀ and spectral asymptotics - when the discrete spectrum is infinite. The results may be applied to hamiltonians of all atims, their positive ions and in most cases of two-atom molecules.
Keywords: Schroedinger operator