One-dimensional quantum scattering from multiple Dirac ? - potentials: a Python-based solution

Abstract

In this research, we present a Python-based solution designed to simulate a one-dimensional quantum system that incorporates multiple Dirac delta - potentials. The primary aim of this research is to investigate the scattering problem within such a system. By developing this program, we can generate wave functions throughout the system and compute transmission and reflection amplitudes analytically and numerically for an infinite range of combinations involving potential strengths, potential separations, and the number of potential centers in the form of the Dirac delta - functions. Furthermore, by modifying the code, we investigate the so-called 'transmission resonances' which yields the energy of the quantum particles undergoing a perfect transmission. Subsequently, our research is extended by considering impurities in the system.