Superluminal Hydrogen Atom in a Constant Magnetic Field in (3+1)-dimensional Spacetime (II)
Emmanuel D. K. Gazoya *
Department of National Nuclear Research Institute (NNRI), Accelerator Research Center (ARC), P.O. Box LG 80, Ghana Atomic Energy Commission (GAEC), Accra, Ghana.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Single-particle interpretation of the plane free Dirac wave, free Dirac particles