Coherent states and excitation of a charged particle in a constant magnetic field by means of an electric field

New integrals of motion, coherent states, the Green's function, and the amplitudes for a transition between the Landau levels are constructed for a nonrelativistic charged particle moving in a time-independent and spatially uniform magnetic field perpendicular to an alternating electric field. It is shown that the dynamic symmetry group of the problem is $U(2,1)$.