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

Translations between Quaternion and Complex Quantum Mechanics

While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a {\em partial} set of {\em translations} may be made. We define these translations and use the rules to obtain rapid quaternion counterparts (some of which are new) of standard quantum mechanical results.Comment: 15 pages, LaTeX, ULTH-93-3

Wave packets and quantum oscillations

We give a detailed analysis of the oscillation formula within the context of the wave packet formalism. Particular attention is made to insure flavor eigenstate creation in the physical cases (Delta p not equal 0). This requirement imposes non instantaneous particle creation in all frames. It is shown that the standard formula is not only exact when the mass wave packets have the same velocity, but it is a good approximation when minimal slippage occurs. For more general situations the oscillation formula contains additional arbitrary parameters, which allows for the unknown form of the wave packet envelope.Comment: 15 pages [8 figs], AMS-Te

REPLY TO HEP-PH/0211241 "On the extra factor of two in the phase of neutrino oscillations"

Arguments continue to appear in the literature concerning the validity of the standard oscillation formula. We point out some misunderstandings and try to explain in simple terms our viewpoint.Comment: 4 pages [1 colored LaTex-fig], AMS-Te

The cosmological dependence of weak interactions

A model for the cosmological time dependence of weak interactions is discused and some experimental tests suggested

Representations of U(1,q) and Constructive Quaternion Tensor Products

The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory. As a consequence, from purely group theoretical arguments we demonstrate that the eigenvalues must be right-eigenvalues and that the only consistent scalar products are the complex ones. We also define an explicit quaternion tensor product which leads to a set of additional group representations for integer ``spin''.Comment: 28 pages, Latex, Dipartimento di Fisica, Universita di Lecce INFN-Sezione di Lecc

Barrier Paradox in the Klein Zone

We study the solutions for a one-dimensional electrostatic potential in the Dirac equation when the incoming wave packet exhibits the Klein paradox (pair production). With a barrier potential we demonstrate the existence of multiple reflections (and transmissions). The antiparticle solutions which are necessarily localized within the barrier region create new pairs with each reflection at the potential walls. Consequently we encounter a new paradox for the barrier because successive outgoing wave amplitudes grow geometrically.Comment: 10 page