The asymptotics of discrete spectrum for the Schroedinger operator in electric and homogeneous magnetic fields

One studies the asymptotics of bound states below the bottom of essential spectrum for the Schroedinger operator in a homogeneous magnetic and a decreasing electric fields. The electric potential is not assumed to be nonpositive. The potential integrated along the direction of magnetic field is supposed to have a power-like behaviour at infinity. The asymptotics of bound states is shown to be of a power-like character, its main term is evaluated.