1,911 research outputs found
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
The Quaternionic Dirac Lagrangian
We discuss the use of the variational principle within quaternionic quantum
mechanics. This is non-trivial because of the non commutative nature of
quaternions. We derive the Dirac Lagrangian density corresponding to the
two-component Dirac equation. This Lagrangian is complex projected as
anticipated in previous articles and this feature is necessary even for a
classical real Lagrangian.Comment: LaTex (9 pages
Tunnelling Through Two Barriers
Recent studies of the tunnelling through two opaque barriers claim that the
transit time is independent of the barrier widths and of the separation
distance between the barriers. We observe, in contrast, that if multiple
reflections are allowed for correctly (infinite peaks) the transit time between
the barriers appears exactly as expected.Comment:
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
Planar Dirac diffusion
We present the results of the planar diffusion of a Dirac particle by step
and barrier potentials, when the incoming wave impinges at an arbitrary angle
with the potential. Except for right-angle incidence this process is
characterized by the appearance of spin flip terms. For the step potential,
spin flip occurs for both transmitted and reflected waves. However, we find no
spin flip in the transmitted barrier result. This is surprising because the
barrier result may be derived directly from a two-step calculation. We
demonstrate that the spin flip cancellation indeed occurs for each particle
(wave packet) contribution.Comment: 6 pages, 2 figure
Quaternion Higgs and the Electroweak Gauge Group
We show that, in quaternion quantum mechanics with a complex geometry, the
minimal four Higgs of the unbroken electroweak theory naturally determine the
quaternion invariance group which corresponds to the Glashow group.
Consequently, we are able to identify the physical significance of the
anomalous Higgs scalar solutions. We introduce and discuss the complex
projection of the Lagrangian density.Comment: 14 pages, LaTex, nofigures, to appear in Int.J.of Mod.Phys.
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