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Double symmetrization and the linearly independent spin eigenfunctions
Author(s) -
Lim T. K.
Publication year - 1986
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560290602
Subject(s) - symmetrization , eigenfunction , spin (aerodynamics) , physics , electron , quantum mechanics , quantum , mathematics , mathematical analysis , eigenvalues and eigenvectors , thermodynamics
It is shown that the exclusion principle merely requires the electrons to be divided into two distinct groups, then, according to our assumption of the distinguishability of electrons, its mathematical representation can be the spatial double antisymmetrization or the spatial‐spin antisymmetrization; in the latter case an auxiliary spin double symmetrization is also required in order to distinguish the two types of electrons. The second requirement is used to recognize the fact that, although all electrons can be assumed to be indistinguishable under certain condition, their natural characteristic of two distinct groups must still be preserved.It is further shown that the double antisymmetrization (or double symmetrization) determines the spin quantum number M , whereas the Löwdin spin projector for nonorthogonal eigenfunctions and the Wigner matric basis for orthogonal eigenfunctions will decide the spin quantum number S , Both the spatial double antisymmetrizer and the spin double symmetrizer will reject all the unnecessary eigenfunctions and project out only one unique set of linearly independent eigenfunctions.