Superluminal Hydrogen Atom in a Constant Magnetic Field in (3+1)-dimensional Spacetime (II)

As has usually been the case in the tradition of some scientific novel ideas, we use the hydrogen
atom as a “test particle”, in the context of superluminal dynamical system theory. In Paper (I) of
this series, the fundamental effect of an applied external magnetic field on a transversely guided
beam of hydrogen-like atoms is uncovered, that of transformation from spherical wave expansion into
plane wave function. This leads to an unprecedented concept of a planar helical hydrogen field,
with a continuum of linear momentum in (3+1)-dimensional spacetime. Thereupon, we investigate
a possible “superluminality” of this field. It turns out that, as in the case of a free Dirac field, the
Dirac-hydrogen field accords with the law of conservation of energy and momentum. As a result, the
generalized translational velocity component expectation value of the planar Dirac-hydrogen is found
to exceed the speed of light, with however, a subluminal minimal velocity.