6533b7d3fe1ef96bd12609ca

RESEARCH PRODUCT

Perfectly matched layers for the stationary Schrodinger equation in a periodic structure

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We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite length and show that solution to this problem approximates a solution to the original problem with an error that exponentially tends to zero as the length of perfectly matched layer tends to infinity.