Four-Dimensional Electron Density Function

IT IS WELL KNOWN THAT THE ENERGY, DIPOLE MOMENT, AND MANY OTHER PROPERTIES OF AN ATOM OR MOLECULE CAN BE CALCULATED IF THE PAIR DENSITY MATRIX, A FUNCTION OF 12 VARIABLES, IS AVAILABLE. For a system with N electrons and therefore 3N degrees of freedom, this is a great simplification, at least in principle if not yet in practice. It does not seem to be known, however, that the 3N dimensional problem can actually be reduced to one in not 12 but four dimensions. A general system of N electronsAND NUCLEI, THE LATTER CONSIDERED AS FIXED IS TREATED. (Author)