Abstract
The completeness of the set is a fundamental requirement of quantum mechanics. The violation of this requirement can lead to significant uncertainty of the physical interpretation of research results in the field of spectral characteristics of many-electron atoms, atomic ions and molecules. In the context of a nonrelativistic one-configurational Hartree–Fock approximation we suggested the solution of the problem of receiving the total complete set of one-particle states of many-electron atoms, including the states of a continuous spectrum. As an accompanying result we introduced the conception of an extended Hilbert space with reflection into mathematical formalism of quantum-mechanical atom description.
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