Authors: Steven Kenneth Kauffmann
The commutator of the Dirac free-particle's velocity operator with its Hamiltonian operator is nonzero and independent of Planck's constant, which starkly violates the quantum correspondence-principle requirement that commutators of observables must vanish when Planck's constant vanishes, as well as violating the extended Newton's First Law principle that relativistic free particles do not accelerate. The consequent nonphysical particle "zitterbewegung" is of course absent altogether when the natural relativistic free-particle square-root Hamiltonian operator, which is the transparent consequence of the free particle's Lorentz-covariant energy-momentum, replaces the free-particle Dirac Hamiltonian. The energy spectrum of the pathology-free relativistic square-root free-particle Hamiltonian is, however, matched perfectly by the positive-energy sector of the Dirac free-particle Hamiltonian's energy spectrum. But when a hydrogen type of potential energy is added to the free particle Dirac Hamiltonian, Foldy-Wouthuysen unitary transformation of the result reveals a "Darwin term" in its positive-energy sector which stems from nonphysical "zitterbewegung"-smearing of that potential energy. This physically nonexistent smearing of the potential energy can alternatively be viewed as having been produced by physically nonexistent smearing of its proton charge density source, which using the Dirac theory for data analysis erroneously compensates, resulting in a misleadingly contracted impression of the proton's charge radius.
Comments: 5 Pages.
[v1] 2019-05-26 09:42:24
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