Remarks on the Complexity of the Schroedinger Equation

The solutions of the electronic Schroedinger equation are high-dimensional objects depending on 3N variables, three for each of the N electrons under consideration. It is therefore rather surprising that simple expansions of the electronic wave functions can be constructed whose convergence rate, measured in terms of the number of determinants involved, is independent of the number of electrons and does not fall below that for a two- or even that for a one-electron system approximated in the same way. In this sense, the complexity of the electronic Schroedinger equation does not exceed that of an equation in three space dimensions. A short report on these developments is given.