Exact convolution-type transparent boundary conditions with a Bessel kernel are derived for the semi-discrete Schrödinger equation, and the continuous limit is recovered.
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Transparent boundary conditions for the spatially discrete Schr\"odinger equation: Reflectionless quantum transport in 1D lattices
Exact convolution-type transparent boundary conditions with a Bessel kernel are derived for the semi-discrete Schrödinger equation, and the continuous limit is recovered.