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

Amplification of coupling for Yukawa potentials

It is well known that Yukawa potentials permit bound states in the Schrodinger equation only if the ratio of the exchanged mass to bound mass is below a critical multiple of the coupling constant. However, arguments suggested by the Darwin term imply a more complex situation. By numerically studying the Dirac equation with a Yukawa potential we investigate this amplification effect.Comment: 7 pages, 2 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.

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: