Partial Waves for a Single Muffin-Tin

We begin by approximating the crystal potential v(r) appearing in the Schro-dinger equation (1.4) by a so-called muffin-tin potential which is defined to be spherically symmetric within spheres of radius S j and to have a constant value the muffin-tin zero, in the interstitial region between 

In the following we consider for simplicity a crystal with one atom per primitive cell, and within a single muffin-tin well (Fig.5.1) we define the potenti al 

Here v(r) is the spherically symmetric part of the crystal potential. The Hamiltonian minus the energy for a system of superimposed muffin-tin wells is 

For reasons of notation we have included a phase factor i, and the spherical harmonics Y (r) have the phase defined by Condon and Shortley [5.3]. Inside the muffin-tin well the radial part p (E,r) must be regular at the 

In the region of constant potential the solutions of (5.4) are spherical waves with wave number k, and their radial parts satisfy (5.6) with vMT(r) = 0, i.e. 

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