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arXiv · 1205.3972

Exact propagators on the lattice with applications to diffractive effects

Emerson Sadurní
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Abstract

The propagator of the discrete Schr\"odinger equation is computed and its properties are revealed through a Feynman path summation in discrete space. Initial data problems such as diffraction in discrete space and continuous time are studied analytically by the application of the new propagator. In the second part of this paper, the analogy between time propagation and 2D scattering by 1D obstacles is explored. New results are given in the context of diffraction by edges within a periodic medium. A connection with tight-binding arrays and photonic crystals is indicated.

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Emerson Sadurní. 2012-05-17. Exact propagators on the lattice with applications to diffractive effects. https://doi.org/10.1088/1751-8113/45/46/465302

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