8,277 research outputs found
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
Right eigenvalue equation in quaternionic quantum mechanics
We study the right eigenvalue equation for quaternionic and complex linear
matrix operators defined in n-dimensional quaternionic vector spaces. For
quaternionic linear operators the eigenvalue spectrum consists of n complex
values. For these operators we give a necessary and sufficient condition for
the diagonalization of their quaternionic matrix representations. Our
discussion is also extended to complex linear operators, whose spectrum is
characterized by 2n complex eigenvalues. We show that a consistent analysis of
the eigenvalue problem for complex linear operators requires the choice of a
complex geometry in defining inner products. Finally, we introduce some
examples of the left eigenvalue equations and highlight the main difficulties
in their solution.Comment: 24 pages, AMS-Te
Quaternionic potentials in non-relativistic quantum mechanics
We discuss the Schrodinger equation in presence of quaternionic potentials.
The study is performed analytically as long as it proves possible, when not, we
resort to numerical calculations. The results obtained could be useful to
investigate an underlying quaternionic quantum dynamics in particle physics.
Experimental tests and proposals to observe quaternionic quantum effects by
neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te
Potential Scattering in Dirac Field Theory
We develop the potential scattering of a spinor within the context of
perturbation field theory. As an application, we reproduce, up to second order
in the potential, the diffusion results for a potential barrier of quantum
mechanics. An immediate consequence is a simple generalization to arbitrary
potential forms, a feature not possible in quantum mechanics.Comment: 7 page
Quaternionic Electroweak Theory
We explicitly develop a quaternionic version of the electroweak theory, based
on the local gauge group . The need of a complex
projection for our Lagrangian and the physical significance of the anomalous
scalar solutions are also discussed.Comment: 12 pages, Revtex, submitted to J. Phys.
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
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
Dirac Equation Studies in the Tunnelling Energy Zone
We investigate the tunnelling zone V0 < E < V0+m for a one-dimensional
potential within the Dirac equation. We find the appearance of superluminal
transit times akin to the Hartman effect.Comment: 12 pages, 4 figure
Quaternionic Electroweak Theory and CKM Matrix
We find in our quaternionic version of the electroweak theory an apparently
hopeless problem: In going from complex to quaternions, the calculation of the
real-valued parameters of the CKM matrix drastically changes. We aim to explain
this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published
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