The motion of the Schrödinger charged particle in a homogeneous, rotating magnetic field represents an exactly soluble model of the Schrödinger quantum dynamics. The Heisenberg motion trajectories are found and classified. It turns out that the rotating magnetic field of not too high intensity/frequency ratio forms a kind of trap, confining the nonrelativistic charged particle into a quasiperiodic motion. As the intensity/frequency ratio crosses a stability threshold, a sudden qualitative change of the Heisenberg trajectory occurs and the particle is expulsed out of the trap. It is shown that for some values of physical parameters our exact model simulates the behavior of the Schrödinger electron in the laser beam traps.