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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Computational nanotechnology</journal-id><journal-title-group><journal-title xml:lang="en">Computational nanotechnology</journal-title><trans-title-group xml:lang="kk"><trans-title>Computational nanotechnology</trans-title></trans-title-group><trans-title-group xml:lang="pt"><trans-title>Computational nanotechnology</trans-title></trans-title-group><trans-title-group xml:lang="ru"><trans-title>Computational nanotechnology</trans-title></trans-title-group><trans-title-group xml:lang="zh"><trans-title>Computational nanotechnology</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2313-223X</issn><issn publication-format="electronic">2587-9693</issn><publisher><publisher-name xml:lang="en">YUR-VAK</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">651722</article-id><article-id pub-id-type="doi">10.33693/2313-223X-2024-11-3-125-160</article-id><article-id pub-id-type="edn">QFISKE</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>MATHEMATICAL MODELING, NUMERICAL METHODS AND COMPLEX PROGRAMS</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ, ЧИСЛЕННЫЕ МЕТОДЫ И КОМПЛЕКСЫ ПРОГРАММ</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Fractals in quantum mechanics: from theory to practical applications</article-title><trans-title-group xml:lang="ru"><trans-title>Фракталы в квантовой механике: от теории к практическим применениям</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6964-9260</contrib-id><contrib-id contrib-id-type="spin">3026-2619</contrib-id><name-alternatives><name xml:lang="en"><surname>Rakhimov</surname><given-names>Rustam Kh.</given-names></name><name xml:lang="ru"><surname>Рахимов</surname><given-names>Рустам Хакимович</given-names></name></name-alternatives><address><country country="UZ">Uzbekistan</country></address><bio xml:lang="en"><p>Dr. Sci. (Eng.), Head, Laboratory No. 1</p></bio><bio xml:lang="ru"><p>доктор технических наук, заведующий, лаборатория № 1</p></bio><email>rustam-shsul@yandex.com</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Institute of Materials Science of the Academy of Science of Uzbekistan</institution></aff><aff><institution xml:lang="ru">Институт материаловедения Академии наук Республики Узбекистан</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2024-08-15" publication-format="electronic"><day>15</day><month>08</month><year>2024</year></pub-date><volume>11</volume><issue>3</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>125</fpage><lpage>160</lpage><history><date date-type="received" iso-8601-date="2025-02-02"><day>02</day><month>02</month><year>2025</year></date><date date-type="accepted" iso-8601-date="2025-02-02"><day>02</day><month>02</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2024, Yur-VAK</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2024, Юр-ВАК</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="en">Yur-VAK</copyright-holder><copyright-holder xml:lang="ru">Юр-ВАК</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://journals.eco-vector.com/2313-223X/about/editorialPolicies</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.eco-vector.com/2313-223X/article/view/651722">https://journals.eco-vector.com/2313-223X/article/view/651722</self-uri><abstract xml:lang="en"><p>This article examines the use of fractals to estimate the probability of classical events controlled by quantum processes. A hypothesis explaining the opposite charges of the positron and electron is discussed, as well as the relationship with the main modern theories of quantum mechanics, such as quantum electrodynamics (QED), string theory, etc. The relationship with the tunnel effect and the pulsed tunnel effect is considered. Examples of practical application of fractals are given, for example, in photocatalysts. The concepts of the effective mass of a photon and the quantum nature of elementary particles, the idea of their internal structure and the formation of matter from the point of view of quantum mechanics are touched upon. Particular attention is paid to the fractal structure of the quantum field as a probability associated with the formation of a positron or electron, and the mathematical connection with the Dirac equation, QED and the Schrödinger equation.</p></abstract><trans-abstract xml:lang="ru"><p>Данная статья рассматривает использование фракталов для оценки вероятности классических событий, управляемых квантовыми процессами. Обсуждается гипотеза об объяснении противоположности зарядов позитрона и электрона, а также взаимосвязь с основными современными теориями квантовой механики, такими как квантовая электродинамика (КЭД), теория струн и др. Рассматривается связь с туннельным эффектом и импульсным туннельным эффектом. Приводятся примеры практического применения фракталов, например, в фотокатализаторах. Затрагиваются понятия эффективной массы фотона и квантовой природы элементарных частиц, идея об их внутренней структуре и формировании материи с точки зрения квантовой механики. Особое внимание уделяется фрактальной структуре квантового поля, как вероятности, связанной с образованием позитрона или электрона, и математической связи с уравнением Дирака, КЭД и уравнением Шрёдингера.</p></trans-abstract><kwd-group xml:lang="en"><kwd>fractals</kwd><kwd>quantum processes</kwd><kwd>positron</kwd><kwd>electron</kwd><kwd>quantum mechanics</kwd><kwd>QED</kwd><kwd>string theory</kwd><kwd>tunnel effect</kwd><kwd>photocatalysts</kwd><kwd>effective photon mass</kwd><kwd>elementary particles</kwd><kwd>quantum field</kwd><kwd>Dirac equation</kwd><kwd>Schrödinger equation</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>фракталы</kwd><kwd>квантовые процессы</kwd><kwd>позитрон</kwd><kwd>электрон</kwd><kwd>квантовая механика</kwd><kwd>КЭД</kwd><kwd>теория струн</kwd><kwd>туннельный эффект</kwd><kwd>фотокатализаторы</kwd><kwd>эффективная масса фотона</kwd><kwd>элементарные частицы</kwd><kwd>квантовое поле</kwd><kwd>уравнение Дирака</kwd><kwd>уравнение Шрёдингера</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Rakhimov R.Kh. 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