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2 votes

Plane wave basis functions

It does not matter: the coeficients are supposed to be complex, absorbing the phases.
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4 votes

Plane-wave basis expansion for periodic material modelling: cutoff energy inequality and number of atoms in the simulation

You’re quite right: as written, the equation is dimensionally inconsistent. There are actually a bunch of constants that make the units work out, but it is customary in matter modeling to define units ...
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