The magnetic moment of free electrons

It is generally believed that many of the properties of solid bodies could be determined theoretically to very good approximation if it were possible to solve completely the Schrodinger wave equation for the motion of an electron in a solid. It is presupposed that the forces in solids are known, and that the effect of the lattice and other electrons on the motion of a single electron can be included in some periodic potential function having the periodicity of the lattice. Usually, this potential function is unknown, but the fact that it has the periodicity of the lattice is sufficient to determine many of the characteristic properties of the solid. We know that the wave function for the motion of an electron through the lattice is that of an infinite plane wave with a function having the lattice periodicity as amplitude, and that the corresponding energies are distributed in bands or zones, the structure of which is determined for each lattice by its particular periodicity

The electrostatic energies of some distorted spherical shells

It is proposed to present here a calculation of the electrostatic energies of some charged spherical shells distorted symmetrically about an axis by functions of the zonal harmonics. Coincidentally, the surface areas of several such istorted spheres are obtaine