Application of quantum theory of electrons to the mechanical and thermal properties of metals

Abstract

The first successful application of quantum mechanics to the problem of metallic cohesion was made by Wigner and Seitz (1938) They appoximated sodium metal by a number of isolated spheres of equal atomic volume and integrated, for various values of the radius of the sphere, the Schrödinger wave equation for the valence electron with the boundary condition that the derivative of the wave function should vanish at the surface of the sphere. To obtain the energy per atom of the metal, they further corrected the energy of the sphere by the mean Fermi energy of free electrons. From the resultant dependence of the energy on the radius of the sphere, they derived the lattice constant, the heat of sublimation per atom, and also roughly the compressibility.