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The APW method was developed by Slater in 1937. Since the effective crystal potential was found
to be constant in most of the open spaces between the cores, the APW method begins by assuming
such a muffintin potential. The potential is that of a
free ion at the core, and is strictly constant outside the core. The wave function for the wave vector
is now taken to be

(242) 
where is the core radius. Outside the core the function is a plane wave because the potential is
constant there. Inside the core the function is atomlike, and is found by solving the appropriate
freeatom Schrödinger equation. Also, the atomic function is chosen such that it joins
continuously to the plane wave at the surface of the sphere forming the core; this is the boundary
condition here.
Notice that there is no constraint relating and for a planewave, since we have
. It is the boundary conditions that determine the value of for a given .
Subsections
Next: Matching the boundary conditions
Up: Methods for bandstructure calculations
Previous: The Muffintin potential
Adrian E. Feiguin
20091104