{"id":1072,"date":"2023-01-09T14:05:16","date_gmt":"2023-01-09T17:05:16","guid":{"rendered":"https:\/\/revistabrasileiradefisica.com\/rbf\/?p=1072"},"modified":"2023-09-01T19:55:30","modified_gmt":"2023-09-01T22:55:30","slug":"um-ensaio-a-matematica-da-mecanica-quantica","status":"publish","type":"post","link":"https:\/\/revistabrasileiradefisica.com\/rbf\/2023\/01\/09\/um-ensaio-a-matematica-da-mecanica-quantica\/","title":{"rendered":"Um Ensaio \u00e0 Matem\u00e1tica da Mec\u00e2nica Qu\u00e2ntica"},"content":{"rendered":"\r\n

An Essay on the Mathematics of Quantum Mechanics<\/em><\/h4>\r\n\r\n\r\n\r\n

DOI<\/strong>: 10.5281\/zenodo.7507996<\/a><\/em><\/p>\r\n\r\n\r\n\r\n

Sebasti\u00e3o Nelson de Ara\u00fajo Martins Filho<\/strong>
ORCID<\/a> | <\/em> Lattes<\/a> | <\/em> E-mail<\/a><\/em><\/p>\r\n\r\n\r\n\r\n

Resumo: <\/strong>A incapacidade da Mec\u00e2nica Cl\u00e1ssica explicar alguns fen\u00f4menos experimentais que estavam sendo realizados no final do s\u00e9culo XIX e in\u00edcio do s\u00e9culo XX, fez com que se iniciasse o desenvolvimento de uma nova teoria f\u00edsica. Cientistas estavam percebendo que a n\u00edvel at\u00f4mico e subat\u00f4mico, a F\u00edsica conhecida at\u00e9 ent\u00e3o, estava falhando. Novas ideias, postulados e interpreta\u00e7\u00f5es come\u00e7aram a aparecer para explicar tais fen\u00f4menos. Com o passar dos anos, ent\u00e3o, surgiu o que hoje conhecemos como Mec\u00e2nica Qu\u00e2ntica. Aparentemente, uma teoria separada da Mec\u00e2nica Cl\u00e1ssica. Mais posteriormente, compreendida como uma extens\u00e3o desta \u00faltima. O presente trabalho \u00e9 uma introdu\u00e7\u00e3o aos principais conceitos e f\u00f3rmulas matem\u00e1ticas usadas nessa \u00e1rea da F\u00edsica, considerando apenas os casos unidimensionais. As ideias apresentadas, em sua maioria, ter\u00e3o mais embasamento matem\u00e1tico do que emp\u00edrico. Tentou-se, tamb\u00e9m, apresentar uma descri\u00e7\u00e3o detalhada nas contas e equa\u00e7\u00f5es, evidenciando-se praticamente todos os passos realizados. A Mec\u00e2nica Qu\u00e2ntica \u00e9 uma \u00e1rea significativamente grande da F\u00edsica, possui expressivo refinamento matem\u00e1tico e v\u00e1rias formas de abordagem. De forma que h\u00e1 uma limita\u00e7\u00e3o de t\u00f3picos a serem apresentados dentro do artigo. Contudo, se espera que, com essa introdu\u00e7\u00e3o, o leitor consiga adquirir uma no\u00e7\u00e3o f\u00edsica e matem\u00e1tica o suficiente para saber como se deve pensar e quais ferramentas utilizar, quando se estuda part\u00edculas muito pequenas.
Palavras-chave:<\/strong> mec\u00e2nica qu\u00e2ntica, f\u00edsica qu\u00e2ntica, f\u00edsica matem\u00e1tica.<\/p>\r\n\r\n\r\n\r\n

Abstract: <\/strong>The inability of Classical Mechanics to explain some phenomena that occurred in scientific experiments that were being carried out in the late 19th and early 20th centuries, led to the development of a new physical theory. Scientists were realizing that at the atomic and subatomic level, hitherto known physics was failing. Thus, new ideas, postulates and interpretations began to be made in order to explain such empirical results. Then over the years, what we now know as Quantum Mechanics emerged; apparently a separate theory from classical mechanics. Later, it was understood as an extension of the latter. The present work is an introduction to the main concepts and mathematical formulas used in this area of Physics, considering only the one-dimensional cases. The ideas presented here, for the most part, will have more mathematical than empirical basis. It was also tried to present a detailed description of the calculations and equations, showing practically all the steps performed. Quantum Mechanics is a significantly large area of Physics, has expressively mathematical refinement and several approaches. Thus there is a limitation of topics to be presented within the article. However, it is hoped that, with this introduction, the reader will be able to acquire enough physical and mathematical notions to know how to think and what tools to use when studying very small particles.<\/em>
Keywords: <\/strong>quantum mechanics, quantum physics, mathematical physics.<\/em><\/p>\r\n\r\n\r\n\r\n

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An Essay on the Mathematics of Quantum Mechanics DOI: 10.5281\/zenodo.7507996 Sebasti\u00e3o Nelson de Ara\u00fajo Martins FilhoORCID | Lattes | E-mail Resumo: A incapacidade da Mec\u00e2nica […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[283],"tags":[292,92,294,202,206,293,291,385],"_links":{"self":[{"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/posts\/1072"}],"collection":[{"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/comments?post=1072"}],"version-history":[{"count":1,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/posts\/1072\/revisions"}],"predecessor-version":[{"id":1073,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/posts\/1072\/revisions\/1073"}],"wp:attachment":[{"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/media?parent=1072"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/categories?post=1072"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/tags?post=1072"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}