Numerical results a quantum waveguide with Mixed boundary conditions

Abstract

This article is devoted to the numerical study of the existence of the eigenvalues of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ in the presence of an electric field of constant intensity $F$ in the direction perpendicular to the electron plane. We impose Neumann boundary conditions on a disc window of radius $a$ and Dirichlet boundary conditions on the remaining part of the boundary of the strip.