Standard Operators

Several standard operators are defined. Once specific spin-orbitals are grouped in shells and we assigned quantum numbers to them operators can be created. The most obvious example is to relate a set of spin-orbitals to an atomic like shell with a radial wave-function times an angular dependent part that is given by the spherical Harmonics. In this case we can talk about the angular momentum and Coulomb interaction in terms of Slater integrals. Although for real molecules and solids the important Wannier orbitals are not given as spherical functions, one very often can take spherical functions as a basis set. (The Gaussian basis set for example works with atom centered spherical harmonic times a radial wave-function).