6 research outputs found
Quaternionic Wave Packets
We compare the behavior of a wave packet in the presence of a complex and a
pure quaternionic potential step. This analysis, done for a gaussian
convolution function, sheds new light on the possibility to recognize
quaternionic deviations from standard quantum mechanics.Comment: 9 pages, 1 figur
Quaternionic Diffusion by a Potential Step
In looking for qualitative differences between quaternionic and complex
formulations of quantum physical theories, we provide a detailed discussion of
the behavior of a wave packet in presence of a quaternionic time-independent
potential step. In this paper, we restrict our attention to diffusion
phenomena. For the group velocity of the wave packet moving in the potential
region and for the reflection and transmission times, the study shows a
striking difference between the complex and quaternionic formulations which
could be matter of further theoretical discussions and could represent the
starting point for a possible experimental investigation.Comment: 10 pages, 1 figur
Wave and Particle Limit for Multiple Barrier Tunneling
The particle approach to one-dimensional potential scattering is applied to
non relativistic tunnelling between two, three and four identical barriers. We
demonstrate as expected that the infinite sum of particle contributions yield
the plane wave results. In particular, the existence of resonance/transparency
for twin tunnelling in the wave limit is immediately obvious. The known
resonances for three and four barriers are also derived. The transition from
the wave limit to the particle limit is exhibit numerically.Comment: 15 pages, 3 figure
Analytic Plane Wave Solutions for the Quaternionic Potential Step
By using the recent mathematical tools developed in quaternionic differential
operator theory, we solve the Schroedinger equation in presence of a
quaternionic step potential. The analytic solution for the stationary states
allows to explicitly show the qualitative and quantitative differences between
this quaternionic quantum dynamical system and its complex counterpart. A brief
discussion on reflected and transmitted times, performed by using the
stationary phase method, and its implication on the experimental evidence for
deviations of standard quantum mechanics is also presented. The analytic
solution given in this paper represents a fundamental mathematical tool to find
an analytic approximation to the quaternionic barrier problem (up to now solved
by numerical method).Comment: 15 pages, 2 figure
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