10 research outputs found
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
Survival law in a potential model
The radial equation of a simple potential model has long been known to yield
an exponential decay law in lowest order (Breit-Wigner) approximation. We
demonstrate that if the calculation is extended to fourth order the decay law
exhibits the quantum Zeno effect. This model has further been studied
numerically to characterize the extra exponential time parameter which
compliments the lifetime. We also investigate the inverse Zeno effect.Comment: 16 pages, 2 tables, 3 figures, 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