The exchange phenomenon, the symmetric group, and the spin degeneracy problem

A review is given of the development of the theory of the exchange phenomenon, the permutation degeneracy, the exclusion principle, the spin, the valence bond functions, and related problems. The theory is based on the use of the fundamental units of the group algebra, and the solution to the eigenvalue problem is expressed in terms of a super secular equation. The many-electron problem is treated both in spin-free quantum mechanics and with the spin included, and it is shown that both methods lead to identical results. The various types of antisymmetric wave functions of correct total spin are studied, and alternative forms of the optimal solutions are finally discussed.