A class of explicitly time-dependent invariants for time-dependent harmonic oscillators is used to construct simple and elegant representations of the general solution of the equations of motion. Then the results for the oscillator are used to derive representations of the general solution of the equations of motion for a charged particle moving classically in the axially symmetric electromagnetic field consisting of an arbitrarily time-dependent, uniform magnetic field, the associated induced electric field, and the electric field due to an arbitrarily time-dependent, uniform charge distribution. © 1968 The American Physical Society.
