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The Augmented Plane Wave (APW) method, and by extension Linearly-Augmented Plane Wave method are both generalizations of the Muffin Tin Approximation. In both the APW and LAPW methods, the potential $V(r)$ is defined as a piecewise function [1] with a single parameter: the muffin-tin radius $r_\mathrm{MT}$. $$ V(r) = % \begin{cases} \sum_{lm} V_{lm} (r) Y_{...


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