Pedagogical applications of the one-dimensional Schr_dinger equation to proximity effect systems: Comparison of Dirichlet and Neumann boundary conditions

摘要

Proximity effect systems in superconducting films can be modeled by a one-dimensional Schr_dinger equation. Several systems are studied using Dirichlet and Neumann boundary conditions. It is observed that the two boundary conditions have a dramatic effect on the lowest eigenstate allowed in these systems, and this points to unusual behavior for solutions of Schr_dinger equation in certain potential wells and proximity effect systems.