The purpose of this note is to give a survey of some recent work on dispersive estimates for the Schrödinger flow (1) e itH Pc, H = − △ + V on R d, d ≥ 1 where Pc is the projection onto the continuous spectrum of H. V is a real-valued potential that

Abstract. We construct an explicit solution of the Cauchy initial value problem for the timedependent Schrödinger equation for a charged particle with a spin moving in an uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. Some special and limiting cases are outlined. The time-dependent Schrödinger equation 1.