The Kronig-Penney Model

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The Kronig–Penney model is a simple, idealized quantum-mechanical system that consists of an infinite periodic array of square potential barriers. It is often used as a pedagogical model to illustrate how periodic potentials can lead to the formation of electronic energy bands and band gaps. Thanks to the simplicity of the model, it is possible to solve for the band structure exactly, and this solution is shown in this Demonstration.

Contributed by: Michael Croucher (March 2011)
Open content licensed under CC BY-NC-SA



The theory behind the Kronig-Penney model can be found in C. Kittel, Introduction to Solid State Physics, John Wiley & Sons Inc, 2004.

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