Fourth-order energy computational scheme

E. Computational Scheme for the Fourth-Order Energy Terms. . 310... 

A wave-mechanical model of the H atom describes an electron in terms of three quantum numbers. However, in order to account for atomic spectra, it is necessary to assume that the extranuclear electrons are not all concentrated at the lowest energy level, but distributed over several levels as stipulated by a fourth quantum number, postulated to represent a two-level spin system that obeys an exclusion principle. The strict consequence of this observation is that the orbitals of a threefold degenerate level must have the third quantum number with values of w/ = — 1,0,1, which eliminates the possibility of three real functions (all w/ = 0). The simple conclusion is that any computational scheme that operates exclusively on real variables cannot be considered to be quantum mechanical, but rather as strictly classical. 

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