Conventional Quantum Statistics with a Probability Distribution Describing Quantum System States

Conventional Quantum Statistics with a Probability Distribution Describing Quantum System States

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 cal...

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Veröffentlicht in:Physics of particles and nuclei 2020-07, Vol.51 (4), p.772-780
Hauptverfasser: Man’ko, V. I., Man’ko, O. V., Chernega, V. N.
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Physics and Astronomy
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container_title Physics of particles and nuclei
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creator Man’ko, V. I.
Man’ko, O. V.
Chernega, V. N.
description 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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Physics and Astronomy
title Conventional Quantum Statistics with a Probability Distribution Describing Quantum System States
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