Hamiltonian large external potential

The determination of the ground state energy and the ground state electron density distribution of a many-electron system in a fixed external potential is a problem of major importance in chemistry and physics. For a given Hamiltonian and for specified boundary conditions, it is possible in principle to obtain directly numerical solutions of the Schrodinger equation. Even with current generations of computers, this is not feasible in practice for systems of large total number of electrons. Of course, a variety of alternative methods, such as self-consistent mean field theories, also exist. However, these are approximate. 

In general, in the study of systems at equihbrium the main advantage of the semiclassical approaches is that they can be utilized in simulation work by following essentially the same techniques as in the classical case (i.e., one works with Ng particles). Moreover, whenever they can be applied, semiclassical approaches can work excellently and represent a substantial saving in computational effort as compared to the exact PI xP-calculations. On the negative side, even the best semiclassical approaches cannot cope with very large quantum diffraction effects. Actually, they do not capture all the information needed to characterize the quantum system (e.g., some g (r) structures cannot be computed). In the literature of this field there are different names for these pair potentials (e.g., classical effective potentials, semiclassical effective potentials, quantum effective pair potentials, etc.). The absence of external fields will be assumed in this section, and the system will be ruled by the Hamiltonian... 

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