Estudio teórico-computacional del efecto túnel mono dimensional con N-Barreras: aplicación a distancias finitas e infinitas

Abstract

In the present research work, a theoretical-computational study of the effect tunnel mono-dimensional with n-bars of potential is made: application at finite and infinite distances, for which first it was proceeding with an analytical description of this effect through a single potential barrier, using the solutions of the Schrödinger equation, and then make derivations for two, three and the general case of n-potential barriers, whether these barriers are separated at finite distances (separation distance between barriers equal to the width of the barrier) or the case in which these barriers are separated at infinite distances (separation distance much greater than the width of the barrier). As a result of these derivations, a generalization of the transmission and reflection coefficient is obtained for barriers at finite distances and another generalization for barriers at infinite distances. These generalizations, when implemented in the Mathematica software, indicate that the transmission coefficient (tunnel effect) depends on both particle energy, barrier width, and the number of potential barriers, but more interestingly, the transmission coefficient for finite distances is lower than for infinite distances. Finally, an experimental continuation is recommended to these results.