2,138 research outputs found
Half-whole Dimensions in Quaternionic Quantum Mechanics
We introduce {\em half-whole} dimensions for quaternionic matrices and
propose a quaternionic version of the Frobenius-Schur theorem which allows us
to obtain the proper quaternionic dimensionality for the representations of the
Dirac and Duffin-Kemmer-Petiau (DKP) algebras.Comment: 9 pages, Revtex, Prog. Theor. Phys. (to be published
Quaternions and Special Relativity
We reformulate Special Relativity by a quaternionic algebra on reals. Using
{\em real linear quaternions}, we show that previous difficulties, concerning
the appropriate transformations on the space-time, may be overcome. This
implies that a complexified quaternionic version of Special Relativity is a
choice and not a necessity.Comment: 17 pages, latex, no figure
Localized Beams and Dielectric Barriers
Recalling the similarities between the Maxwell equations for a transverse
electric wave in a stratified medium and the quantum mechanical Schroedinger
equation in a piece-wise potential, we investigate the analog of the so called
particle limit in quantum mechanics. It is shown that in this limit the
resonance phenomena are lost since individual reflection and transmission terms
no longer overlap. The result is a stationary zebra-like response with the
intensity in each stripe calculable.Comment: 8 pages, 3 figure
Laser Interaction with a Dielectric Block
Some optical experiments provide the easiest way to test quantum mechanical
predictions. Such a situation applies to a laser beam traversing a dielectric
structure. The dielectric structure mir- roring quantum mechanical potentials.
The simplest of these, studied in this paper, involves a single dielectric
block. We exhibit both by analytic and numerical calculations explicit examples
of total coherence and total incoherence phenomena. Which case appears depends
upon the angle of incidence of the laser beam and/or the dimensions of beam vs
block width. Unlike our previ- ous studies our calculations here are
three-dimensional, although, with suitable approximations, somewhat simpler
planar expressions can be derived.Comment: 14 pages, 3 figure
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