An energy interpretation of exact solutions of Dirac equation in terms of standing waves modes

International audienceSolutions of Dirac equation are well known in terms of bi-spinors, but the complete determination of these spinors is always derived using the assumption that the wave function is a plane wave. We investigate in this paper the search of general solutions under the form of standing wave modes, using methods issued from electromagnetism. It is shown that such solutions exist as solutions of a system of 64 equations and 64 unknowns, and that they must be associated with a relativistic relation of energy conservation. Complete exact solutions are presented. It is shown that these solutions highlight in a new manner the duality wave-particle, and the uncertainty principle