The quantal cumulant dynamics (QCD) method for multi-dimensional cases is developed in order to simulate the model quantum confinement systems under a magnetic field. We feature the resonant levels in quantum wells as found in the classical mechanics, magnetic-field induced tunneling, and magnetic confinement in a model quantum ring nanostructure. Trajectories and position cumulant variables are analyzed in order to characterize these phenomena. We find that (i) the magnetic confinement originates from resonant level trajectories between cycloid and drift motions and (ii) the position cumulant variables decrease during transitions among the wells, which reflects a tunneling motion. (C) 2008 Elsevier B.V. All rights reserved.