Quasi-classical versus non-classical spectral asymptotics for magnetic Schrodinger operators with decreasing electric potentials

consider the Schrodinger operator H(V) 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(V) 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.