The sixth Hilbert's problem and the principles of quantum informatics
| dc.creator | Bogdanov, Yu. I. | |
| dc.date | 2006-12-04 | |
| dc.date.accessioned | 2026-07-07T07:35:07Z | |
| dc.date.available | 2026-07-07T07:35:07Z | |
| dc.description | By 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.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0612025 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0612025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119991 | |
| dc.subject | Quantum Physics | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.title | The sixth Hilbert's problem and the principles of quantum informatics | |
| dc.type | text |