DKP equation with smooth barrier

In this paper, we study the Duffin–Kemmer–Petiau (DKP) equation in the presence of a smooth barrier in dimensions space–time (1+1) dimensions. The eigenfunctions are determined in terms of the confluent hypergeometric function [Formula: see text]. The transmission and reflection coefficients are calculated, special cases as a rectangular barrier and step potential are analyzed. A numerical study is presented for the transmission and reflection coefficients graphs for some values of the parameters [Formula: see text] are plotted.

Insertion loss (IL) of finite sound barriers of different contours - An introduction to geometrical solutions in 3-D space

The design of finite sound barriers noise sources and control points requires calculations beyond those that are used when the Maekawa formula is applied, since the problem involves polygon sd barriers located in various possible orientations in 3D space. We present here some means that are linked to basic mathematical geometrical tools. Those means are relatively simple, as compared to the physical formulation of the relevant diffraction solutions for sound barriers (e.g. Rosenhouse, 2019, 2020). Such calculations can apply algebraic, trigonometric or vector analysis and their combinations to define the geometries of barrier IL. This approach includes the location of the sources and control points, which are essential as data for finding IL and other issues of environmental acoustics. We will show solutions including results of IL for a common rectangular barrier, as compared to IL of a barrier with a sloped top and side, among other possibilities.

Klein paradox for bosons, wave packets and negative tunnelling times

We analyse a little known aspect of the Klein paradox. A Klein–Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism is demonstrably acausal, yet an attempt to construct the corresponding causal solution of the Klein–Gordon equation fails. We relate the causal solution to a divergent multiple-reflections series, and show that the problem is remedied for a smooth barrier, where pair production at the energy equal to a half of the barrier’s height is enhanced yet remains finite.