Atoms in Crystals and Correlation Diagrams

Abstract

Consider an atom with Z protons in its nucleus and with Z outer electrons (the atomic number of the atom is Z). In the central-field approximation, atomic electrons are assumed to be independent of one another. The Hamiltonian of the ith atomic electron is given by

$${H_{i}}({r_{i}}) = \frac{{p_{i}^{2}}}{{2m}} - \frac{{Z{e^{2}}}}{{{r_{i}}}}$$

((6.1a))

which has the eigenstates

$${\Psi _{nlm}}({r_i}) = {R_{nl}}({r_i}){Y_{lm}}({\theta _i},{\phi _i}){\xi _i}$$

((6.1b))