{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T18:49:06Z","timestamp":1760986146364,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,22]],"date-time":"2023-01-22T00:00:00Z","timestamp":1674345600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["19-71-10091"],"award-info":[{"award-number":["19-71-10091"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A short review constructing the probability representation of quantum mechanics is given, and examples of the probability distributions describing the states of quantum oscillator at temperature T and the evolution of quantum states of a charged particle moving in the electric field of an electrical capacitor are considered. Explicit forms of time-dependent integrals of motion, linear in the position and momentum, are used to obtain varying probability distributions describing the evolving states of the charged particle. Entropies corresponding to the probability distributions of initial coherent states of the charged particle are discussed. The relation of the Feynman path integral to the probability representation of quantum mechanics is established.<\/jats:p>","DOI":"10.3390\/e25020213","type":"journal-article","created":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T02:27:45Z","timestamp":1674440865000},"page":"213","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Quantum Oscillator at Temperature T and the Evolution of a Charged-Particle State in the Electric Field in the Probability Representation of Quantum Mechanics"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1282-4560","authenticated-orcid":false,"given":"Margarita A.","family":"Man\u2019ko","sequence":"first","affiliation":[{"name":"Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3972-0227","authenticated-orcid":false,"given":"Vladimir I.","family":"Man\u2019ko","sequence":"additional","affiliation":[{"name":"Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia"},{"name":"Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow 141700, Russia"},{"name":"Russian Quantum Center, Skolkovo, Moscow 143025, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,22]]},"reference":[{"key":"ref_1","unstructured":"Kolmogorov, A.N. 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