Pedagogical applications of the one-dimensional Schrödinger's equation to proximity effect systems: Comparison of Dirichlet and Neumann boundary conditions
arXiv:0901.2894 · doi:10.1119/1.3078414
Abstract
Proximity effect systems in superconducting films can be modeled by a one-dimensional Schrödinger 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 points to unusual behavior for solutions of Schrödinger's equation in certain potential wells and proximity effect systems.
10 pages, 7 figures. To be published in American Journal of Physics