  We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant
magnetic field and electric potential V which typically decays at infinity
exponentially fast or has a compact support. We investigate the asymptotic
behaviour of the discrete spectrum of H near the boundary points of its
essential spectrum. If the decay of V is Gaussian or faster, this behaviour is
non-classical in the sense that it is not described by the quasi-classical
formulas known for the case where V admits a power-like decay.
