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reciprocal space

Space as we know it — the 3-dimensional environment in which we live and in which crystals exist, an environment called direct space in this context — can be represented in a different way as ‘reciprocal space’. Kohn-Sham solvers make use of it a lot.

reciprocal space

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    1. Question

    Consider 3 points in direct space, with coordinates A=(1,1), B=(1,2) and C=(1,3). Calculate the distance between A and B, and between B and C. Now determine the coordinates of these three points in reciprocal space, and find the same two distances in reciprocal space. Based on your observations, assess the statement that “points that lie at similar distances from each other in real space, will lie at similar distances from each other in reciprocal space.”

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