Atomic field equations for Maxwell fields interacting with non-relativistic quantal sources

The microscopic field equations of electromagnetism interacting with a many-particle Schrodinger field of charged particles are shown to be exactly equivalent to the atomic field equations where the sources are free electron and ion charge densities and convective and Rontgen current densities only. The fields are now the microscopic displacement vector d and the microscopic auxiliary field h and their relation to the electric and magnetic fields e and b are given exactly in terms of polarization and magnetization vectors without reference to any multipolar expansions. The values of the polarization fields are calculated for several transitions in atomic hydrogen to illustrate the connexion with the usual multipole expansions.