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The relationship between the topological structure of the multidimensional configuration space and the structure of the symmetrical permutation group SN is analyzed. This relationship permits to separate the spin and spatial variables during the solution of the spinless stationary Schrödinger equation. It is possible to simplify the construction of wave functions for N-electron systems and to expand the class of trial functions in the variation method. The relation of the suggested approach to the construction of wave functions by traditional methods is demonstrated by the example of three-electron systems.

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