A method of approximating the energy states of electrons in a crystal lattice; the potential is assumed to be spherically symmetrical within spheres centered at each atomic nucleus and constant in the interstitial region, wave functions (the augmented plane waves) are constructed by matching solutions of the Schrödinger equation within each sphere with plane-wave solutions in the interstitial region, and linear combinations of these wave functions are then determined by the variational method. Abbreviated APW method.