Exact propagators on the lattice with applications to diffractive effects
Quantum Physics
2012-11-01 v2 Other Condensed Matter
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.
Cite
@article{arxiv.1205.3972,
title = {Exact propagators on the lattice with applications to diffractive effects},
author = {Emerson Sadurní},
journal= {arXiv preprint arXiv:1205.3972},
year = {2012}
}
Comments
Final version with two appendices. Published in J. Phys. A: Math. Theor