Smoothing estimates for the Schrodinger equation with unbounded   potentials
  We prove a local in time smoothing estimate for a magnetic Schrodinger equation with coefficients growing polynomially at spatial infinity. The assumptions on the magnetic field are gauge invariant and involve only the first two derivatives. The proof is based on the multiplier method and no pseudofferential techniques are required. 
Piero D'Ancona, Luca Fanelli