Surface electronic wave functions of a semi-infinite muffin-tin lattice. I. The spherical-wave method

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Abstract
A new method is developed for evaluating the electronic wave functions of a semi-infinite muffin-tin lattice. A secular equation is derived for the amplitudes of the spherical-wave components of the wave function in the interstitial region of the solid. The spherical-wave amplitude equation is solved by expressing the amplitudes as the sum of a finite number of propagating (if appropriate) and slowly decaying normal modes, plus a rapidly decaying residual amplitude. The normal-mode components represent the asymptotic form of the wave function in the bulk solid, and the residual component contributes to the wave function close to the surface plane. The present approach overcomes certain analytical difficulties associated with a beam representation of the wave function in the interstitial region of the solid.