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Conventional Quantum Statistics with a Probability Distribution Describing Quantum System States

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Abstract

The review of a new probability representation of quantum states is presented, where the states are described by conventional probability distribution functions. The invertible map of the probability distribution onto density operators in the Hilbert space is found using the introduced operators called a quantizer–dequantizer, which specify the invertible map of operators of quantum observables onto functions and a product of the operators onto an associative product (star product) of the functions. Examples of a quantum oscillator and a spin-1/2 particle are considered. The kinetic equations for probabilities, specifying the evolution of the states of a quantum system, which are equivalent to Schrödinger and von Neumann equations, are derived explicitly.

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Notes

  1. This work is based on the conference paper presented by V.I. Man’ko at the International Bogolyubov Conference on Problems of Theoretical and Mathematical Physics. The authors dedicate this work to the memory of Academician N.N. Bogolyubov, who was the Chair of the Theory Physics Department at MSU, and from which they graduated.

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Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    V. I. Man’ko, O. V. Man’ko & V. N. Chernega

  2. Moscow Institute of Physics and Technology (State University), 141701, Dolgoprudny, Moscow oblast, Russia

    V. I. Man’ko

  3. Bauman Moscow State Technical University, 105005, Moscow, Russia

    O. V. Man’ko

Authors
  1. V. I. Man’ko
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  2. O. V. Man’ko
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  3. V. N. Chernega
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Correspondence to V. I. Man’ko, O. V. Man’ko or V. N. Chernega.

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Translated by M. Samokhina

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Man’ko, V.I., Man’ko, O.V. & Chernega, V.N. Conventional Quantum Statistics with a Probability Distribution Describing Quantum System States. Phys. Part. Nuclei 51, 772–780 (2020). https://doi.org/10.1134/S1063779620040486

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