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For the remaining terms in Eq. (1-182) we use Eq. (1-190) and write Defining two more abbreviations by (1-198) and (1-199) we finally obtain -e X nLKs &LKt ~~£ X nLKs nLKt — LKt (1-200) (1-192) n LKt L where Next, we use the identity 1 \(DlKs) 1 ^ = S 0t(DlKt) a>lKt - co IKS (1-194) which may be proved directly with the help of the Eqs. (1-168) to (1-170). If we now define the quantity 1 (D1V — (Oi This is the secular equation for the LAPW method, see also Andersen (1975) and (1984).

1-156) and (1-157), where we now imply integration over the unit cell, we easily derive the following result by means of the Schrodinger equation for cf> and <> / (Eqs. (1-162) and (1-163)) and the orthogonality relation (Eq. 3 Linear Augmented Plane Waves (LAPW) With a choice of a plane wave for the envelope function we obtain the LAPW method. The quantum label j becomes a reciprocal lattice vector Ks and Bloch symmetrization (see Eq. (1-154)) is not necessary. \ CJki(k + Ks)-r (\ V\I) — e and augment this plane wave inside the spheres using the angular momentum expansion about the site T exactly as in Sec.

1-280) and would have been obtained by the preceeding steps had we used the simple expression for the matrix element given by Eq. (1-268). We will come back to Eq. (1-285) but first repeat what was called KKR-ASA. This time we will construct energy-dependent orbitals, Xi (£> r% but instead of using solutions of Laplace's equation to formulate the boundary conditions, we will use solutions of the wave equation (1-245), initially employing a fixed value for the energy parameter x=^JV0. Exactly as before (Eq.

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