The sixth Hilbert's problem and the principles of quantum informatics

dc.creatorBogdanov, Yu. I.
dc.date2006-12-04
dc.date.accessioned2026-07-07T07:35:07Z
dc.date.available2026-07-07T07:35:07Z
dc.descriptionBy the example of a Fourier transform, the possibilities of Hilbert space geometry applications for statistical model construction are analyzed. In accordance with Bohr's complementarity principle, mutually-complementary coordinate and momentum representations are presented. It was demonstrated that the characteristic function of coordinate distribution may be considered as a convolution of the psi-function in momentum representation and vice versa. The naturalness of coordinate and momentum operators introduction is demonstrated. A probabilistic interpretation of Hilbert space geometry is given. Cauchy-Bunyakowsky (Cauchy-Schwartz), Cramer-Rao and uncertainty inequalities are considered in the same framework. The principal postulates of quantum informatics as a natural science are presented. It is demonstrated that quantum informatics serves as a theoretic basis for both probability theory and quantum mechanics.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0612025
dc.identifierhttp://arxiv.org/abs/quant-ph/0612025
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119991
dc.subjectQuantum Physics
dc.subjectData Analysis, Statistics and Probability
dc.titleThe sixth Hilbert's problem and the principles of quantum informatics
dc.typetext

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