Separability Problem in General Many Electron Systems

Since few problems of interest admit of solutions in closed form in quantum mechanics, we are obliged to use approximate methods based on expansion schemes of one form or another. Such expansions, when truncated at some finite order, often do not reflect some of the inherent properties of the systems under study. A typical example of this type of failure is the well known “symmetry dilemma” encountered in the Hartree — Fock calculation. The broken- symmetric solutions, occasionally faced, stem from the use of a restricted variation of the function in the subspace of single determinants. A full CI calculation will obviously restore the symmetry, but since that is neither practicable nor desirable, additional conditions are imposed to ensure that the resultant functions are symmetry-adapted even at the trial function level.