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

Details Pedagogical applications of the one-dimensional Schrödinger's equation to proximity effect systems: Comparison of Dirichlet and Neumann boundary conditions Pedagogical applications of the one-dimensional Schrödinger's equation to proximity effect systems: Comparison of Dirichlet and Neumann boundary conditions

2009-01-19

arxiv.org/abs/0901.2894v1

Am. Journal of Phys., Volume 77, 360 (2009)

Physics

Quantum Physics

10 pages, 7 figures. To be published in American Journal of Physics

Scientific paper

10.1119/1.3078414

Proximity effect systems in superconducting films can be modeled by a one-dimensional Schr\"odinger 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 Schr\"odinger's equation in certain potential wells and proximity effect systems.

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