Translational motion general permutation

From the general considerations presented in the previous section, one can expect that the many-body non-adiabatic wave function should fulfill the following conditions (1) All particles involved in the system should be treated equivalently (2) Correlation of the motions of all the particles in the system resulting from Coulombic interactions, as well as from the required conservation of the total linear and angular momenta, should be explicitly incorporated in the wave function (3) Particles can only be distinguishable via the permutational symmetry (4) The total wave function should possess the internal and translational symmetry properties of the system (5) For fixed positions of nuclei, the wave functions should become equivalent to what one obtains within the Born-Oppenheimer approximation and (6) the wave function should be an eigenfunction of the appropriate total spin and angular momentum operators. 

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