Classical and quantum mechanics of a charged particle in oscillating electric and magnetic fields

The motion of a particle with charge q and mass m in a magnetic field given by B = kB(0) + B-1[icos(omega t) + jsin(omega t)] and an electric field wh ich obeys del x E = -partial derivative B/partial derivative t is analyzed classically and quantum-mechanically. The use of a retesting coordinate sys tem allows the analytical derivation of the particle classical trajectory a nd its laboratory wavefunction. The motion exhibits two resonances, one at omega = omega(c) = -qB(0)/m, the cyclotron frequency, and the other at omeg a = omega(L) = -qB(0)/2m, the Larmor frequency. For w at the first resonanc e frequency, the particle acquires a simple closed trajectory, and the effe ctive hamiltonian can be interpreted as that of a particle in a static magn etic field. In the second case a term corresponding to an effective static electric field remains, and the particle orbit is an open line. The particl e wave function and eigenenergies are calculated.