The muffin-tin approximation is a shape approximation of the potential well in a crystal lattice. It is most commonly employed in quantum mechanical simulations of the electronic band structure in solids. The approximation was proposed by John C. Slater. Augmented plane wave method (APW) is a method which uses muffin-tin approximation. It is a method to approximate the energy states of an electron in a crystal lattice. The basic approximation lies in the potential in which the potential is assumed to be spherically symmetric in the muffin-tin region 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. Many modern electronic structure methods employ the approximation. Among them APW method, the linear muffin-tin orbital method (LMTO) and various Green's function methods. One application is found in the variational theory developed by Jan Korringa (1947) and by Walter Kohn and N. Rostoker (1954) referred to as the KKR method. This method has been adapted to treat random materials as well, where it is called the KKR coherent potential approximation.