Adaptable transfer-matrix method for fixed-energy finite-width beams

This work presents a novel methodology to analytically solve the stationary Schrödinger equation in presence of a couple of two-dimensional semi-infinite rectangular potential barriers, when the incident wave is a finite-width monoenergetic wave packet. Such methodology does not depend at all on the incident wavefront of the packet and is based on the transfer-matrix method, but unlike the latter, our transfer matrix is built partly in real space and partly in Fourier space. A spectrum of angular plane waves is used to represent the incident, reflected and transmitted beams. As a particular case, we study the transmission of Hermite-Gaussian wave packets through the barrier system. A detailed analysis of the transmission coefficient is carried out as a function of both the parameters of the incident beam (which in turn are directly related to the shape of the incident packet) and the parameters of the barriers. We also briefly discuss the behavior of the probability density of three transmitted beams. (paper)