dorsal/arxiv
View SchemaThe sixth Hilbert's problem and the principles of quantum informatics
| Authors | Yu. I. Bogdanov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612025 |
| URL | https://arxiv.org/abs/quant-ph/0612025 |
Abstract
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.
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"date_created": "2026-03-02T18:02:34.485000Z",
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"abstract": "By the example of a Fourier transform, the possibilities of Hilbert space\ngeometry applications for statistical model construction are analyzed. In\naccordance with Bohr\u0027s complementarity principle, mutually-complementary\ncoordinate and momentum representations are presented. It was demonstrated that\nthe characteristic function of coordinate distribution may be considered as a\nconvolution of the psi-function in momentum representation and vice versa. The\nnaturalness of coordinate and momentum operators introduction is demonstrated.\nA probabilistic interpretation of Hilbert space geometry is given.\nCauchy-Bunyakowsky (Cauchy-Schwartz), Cramer-Rao and uncertainty inequalities\nare considered in the same framework. The principal postulates of quantum\ninformatics as a natural science are presented. It is demonstrated that quantum\ninformatics serves as a theoretic basis for both probability theory and quantum\nmechanics.",
"arxiv_id": "quant-ph/0612025",
"authors": [
"Yu. I. Bogdanov"
],
"categories": [
"quant-ph",
"physics.data-an"
],
"title": "The sixth Hilbert\u0027s problem and the principles of quantum informatics",
"url": "https://arxiv.org/abs/quant-ph/0612025"
},
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