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Von Neumann in 1932 was the first to outline the possible non-existence of dispersion free ensembles in quantum mechanics, and he used this basic evidence to give a preliminary proof on incompatibility between quantum mechanics and local hidden variables theory. In the present paper, we give a detailed theoretical elaboration on the manner in which such a fundamental subject could be explored at perceptive and cognitive levels in humans. We also discuss a general design of the experiment that we have in progress so to give direct indications to other researchers engaged in such field.

May We Verify Non-Existing Dispersion Free Ensembles By Application of Quantum Mechanics in Experiments at Perceptive and Cognitive Level?