The discretized Schrödinger equation and simple models for semiconductor quantum wells

@article{Boykin2004TheDS,
  title={The discretized Schr{\"o}dinger equation and simple models for semiconductor quantum wells},
  author={Timothy B. Boykin and Gerhard Klimeck},
  journal={European Journal of Physics},
  year={2004},
  volume={25},
  pages={503-514}
}
The discretized Schrodinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schrodinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid… 

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