One-dimensional macro-scale matter wave dynamics potentially embedded in the Lorentz trajectory

We point the rather unusual existence of a potential embedding in the Lorentz trajectory - charged particle trajectory in a magnetic field - of a one-dimensional matter wave dynamics on the macro-scale as demonstrated through one-dimensional matter wave interference effects on the macro-scale, as well as the observation of a curl-free vector potential in one dimension, also on the macro-scale. Such an embedding is a manifestation of the generation of the quantum modulation of the de Broglie wave of the particle along the magnetic field, arising concomitantly, with a scattering-induced transition across Landau levels in consequence of quantum entanglement between the parallel and perpendicular degrees of freedom.