To afford a basis for constructing Thomas-Fermi-like approximations to the electronic structure of atoms in intense applied fields, the canonical density matrix (or equivalently the Feynman propagator) for free electrons is first set up. This is done for both intense magnetic and intense electric fields: in each case, exact results are available for arbitrary static field strengths.
Physical properties of atoms and ions in intense magnetic fields are hence obtained in the statistical limit of Thomas-Fermi theory. This discussion is then supplemented by the ‘hyperstrong’ limit, considered especially by Lieb and co-workers. Chemistry in intense magnetic fields is thereby compared and contrasted with terrestrial chemistry. Some emphasis is then placed on a model of confined atoms in intense electric fields: the statistical Thomas-Fermi approximation again being the central tool employed.