ABSTRACT
The mathematical formulation of the quantum many-body problem (without relativistic corrections) was given by Schro¨dinger in one of his pioneer works.1 Since the wave function sought depends on the great number of variables (namely, there are as many of them as degrees of freedom in the N electron system), the exact solution of this problem encounters the insuperable difficulties and consequently one needs to resort to approximate methods. An extremely ingenious way was proposed by Hartree.2 However, the derivation of the equations given by Hartree himself was based on the consideration not related to the Schro¨dinger equation in the configuration space. Another work by Gaunt3 was devoted to the statement of this link, but the problem was not solved entirely because nothing was mentioned about Hartree’s equations being connected with the variational principle. The main point of Hartree’s method called by him as that of the “self-consistent field” consists of the following. Hartree preserves the classical notion of the individual electron orbit provided each orbit is described, according to Schro¨dinger, by the wave function. For each wave function (i.e., for each individual electron) one constructs the Schro¨dinger equation with the potential energy originating from the interaction first with a nucleus and second with other electrons continuously distributed with the charge density = ψψ.
