English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

This report deals with the basic concepts on deducing transit times forquantum scattering: the stationary phase method and its relation with delaytimes for relativistic and non-relativistic tunneling particles. We notice thatthe applicability of this method is constrained by several subtleties inderiving the phase time that describes the localization of scattered wavepackets. We investigate the general relation between phase times and dwelltimes for quantum tunneling/scattering. Considering a symmetrical collision oftwo identical wave packets with an one-dimensional barrier, we demonstrate thatthese two distinct transit time definitions are explicitly connected. Thetraversal times are obtained for a symmetrized (two identical bosons) and anantisymmetrized (two identical fermions) quantum colliding configuration.Multiple wave packet decomposition shows us that the phase time (group delay)describes the exact position of the scattered particles and, in addition to theexact relation with the dwell time, leads to correct conceptual understandingof both transit time definitions. At last, we extend the non-relativisticformalism to the solutions for the tunneling zone of a one-dimensionalelectrostatic potential in the relativistic (Dirac to Klein-Gordon) waveequation where the incoming wave packet exhibits the possibility of beingalmost totally transmitted through the potential barrier. The conditions forthe occurrence of accelerated tunneling transmission probabilities are allquantified and the problematic superluminal interpretation based on thenon-relativistic tunneling dynamics is revisited.

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles