Reconsidering the validation of multi-electron standard quantitative quantum mechanics
Hypothesis: Multi-electron standard quantitative quantum mechanics (M-SQQM) is not a validated theory. Although the intractable nature of the full mathematical expression prevents solution, the structure of the final form is clear: a fully 3N, where N is the number of electrons,
dimensional function in which: (i) each point has a unique value, (ii) electrons are indistinguishable, (iii) there is only one expectation value, no matter the number of electrons, for energy, radius, etc., (iv) even the highest excited state has an energy tens to thousands of electron volts
below the vacuum level, and (v) the scalar value at each point in 3N space is a component of a configuration probability. (Where are those dimensions?) The intractable nature of the mathematics does require that “approximations,” all dramatically different from M-SQQM theory, be
solved for comparison with energy measurement/validation. All are in 3 dimensions, in every case each point in space has at least N values, and in those cases (nonsymmetrized version) in which the wave function has any physical/probabilistic meaning each electron occupies an independent state
defined by its own eigenvalues, metaphysical descriptions of electron “exchange,” notwithstanding. Cleary these are not approximations, but rather distinct theories; hence, their agreement with data is immaterial to validation of M-SQQM. Other notable issues include: (i) the difficulty
of finding an energy level scheme that simultaneously satisfies the Pauli Exclusion Principle, energy conservation, and measured ionization energies, and (ii) the clearly invalid methods for computing electron‐electron interaction energy for spatially overlapping wave functions. All
of this suggests that a valid quantum theory will have distinguishable electrons with no spatial overlap.
Keywords: Classical Quantum Mechanics; Helium; Multi-Electron Theory; Pauli Exclusion Principle; Quantum Theory
Document Type: Research Article
Affiliations: Physics Department, Naval Postgraduate School, Monterey, California 93943, USA
Publication date: 16 September 2014
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