{"id":9450,"date":"2020-03-25T11:48:12","date_gmt":"2020-03-25T14:48:12","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=9450"},"modified":"2023-04-24T10:02:02","modified_gmt":"2023-04-24T13:02:02","slug":"exemplo-particula-na-caixa","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/exemplo-particula-na-caixa\/","title":{"rendered":"Part\u00edcula na Caixa"},"content":{"rendered":"<p><span style=\"font-family: verdana, geneva, sans-serif;\">A maior dificuldade pr\u00e1tica da <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/fisica-quantica\/equacao-de-schrondinger\/\">Equa\u00e7\u00e3o de Schr\u00f6dinger<\/a> reside na dificuldade de resolu\u00e7\u00e3o de sistemas com muitas part\u00faiculas. Por isso, utilizam-se diversas simplifica\u00e7\u00f5es para analisar sistemas complexos. A <a href=\"https:\/\/en.wikipedia.org\/wiki\/Particle_in_a_box\" target=\"_blank\" rel=\"noopener\">part\u00edcula na caixa<\/a> representa uma dessas simplifica\u00e7\u00f5es.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Para visualizar melhor o significado e implica\u00e7\u00f5es da Equa\u00e7\u00e3o de Schr\u00f6dinger, considera-se o exemplo de uma part\u00edcula em movimento unidimensional dentro de uma caixa &#8211; Fig. 1. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Nesse caso, para manter uma part\u00edcula eletricamente carregada confinada entre os pontos 0 e a, torna-se necess\u00e1rio criar uma barreira de potencial el\u00e9trico infinito nas fronteiras com polaridade contr\u00e1ria \u00e0 da carga.<\/span><\/p>\n<figure id=\"attachment_9359\" aria-describedby=\"caption-attachment-9359\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula-na-caixa.png\"><img decoding=\"async\" class=\"size-full wp-image-9359\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula-na-caixa.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula-na-caixa.png 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula-na-caixa-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula-na-caixa-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-9359\" class=\"wp-caption-text\">Figura 1. Part\u00edcula na caixa<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Matematicamente, isto requer as seguintes condi\u00e7\u00f5es de contorno:<\/span><\/p>\n<figure id=\"attachment_9377\" aria-describedby=\"caption-attachment-9377\" style=\"width: 261px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/p_inbox_1.png\"><img decoding=\"async\" class=\"wp-image-9377 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/p_inbox_1.png\" alt=\"\" width=\"261\" height=\"96\" \/><\/a><figcaption id=\"caption-attachment-9377\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 1. Condic\u00f5es de contorno<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este exemplo transforma a <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/atomos\/fisica-quantica\/equacao-de-schrondinger\/\">Equa\u00e7\u00e3o 6 do Cap\u00edtulo Equa\u00e7\u00e3o de Schr\u00f6dinger<\/a> na seguinte equa\u00e7\u00e3o diferencial. <span id='easy-footnote-1-9450' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/exemplo-particula-na-caixa\/#easy-footnote-bottom-1-9450\" title=\" a maioria dos livros texto sobre mec\u00e2nica qu\u00e2ntica utiliza E para energia cin\u00e9tica e V para energia potencial. Contudo, nem sempre esta energia potencial decorre de campo el\u00e9trico. \"><sup>1<\/sup><\/a><\/span><\/span><\/p>\n<figure id=\"attachment_9402\" aria-describedby=\"caption-attachment-9402\" style=\"width: 735px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_1.png\"><img decoding=\"async\" class=\"wp-image-9402 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_1.png\" alt=\"\" width=\"735\" height=\"96\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_1.png 735w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_1-300x39.png 300w\" sizes=\"(max-width: 735px) 100vw, 735px\" \/><\/a><figcaption id=\"caption-attachment-9402\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 2. Equa\u00e7\u00e3o de Schr\u00f6dinger unidimensional invariante no tempo<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Como o potencial dentro da caixa \u00e9 zero, a Equa\u00e7\u00e3o 2 se transforma em<span id='easy-footnote-2-9450' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/exemplo-particula-na-caixa\/#easy-footnote-bottom-2-9450\" title=\" Uma equa\u00e7\u00e3o diferencial homog\u00eanea linear de segunda ordem &amp;#8211; Cap2 KREYSZIG\"><sup>2<\/sup><\/a><\/span>:<\/span><\/p>\n<figure id=\"attachment_9403\" aria-describedby=\"caption-attachment-9403\" style=\"width: 490px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_2.png\"><img decoding=\"async\" class=\"size-full wp-image-9403\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_2.png\" alt=\"\" width=\"490\" height=\"96\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_2.png 490w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_2-300x59.png 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/a><figcaption id=\"caption-attachment-9403\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 3. Equa\u00e7\u00e3o de Schr\u00f6dinger dentro da caixa<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 4 fornece a solu\u00e7\u00e3o geral da Equa\u00e7\u00e3o 3<\/span><\/p>\n<figure id=\"attachment_9411\" aria-describedby=\"caption-attachment-9411\" style=\"width: 630px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_5.png\"><img decoding=\"async\" class=\"wp-image-9411 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_5.png\" alt=\"\" width=\"630\" height=\"51\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_5.png 630w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_5-300x24.png 300w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/a><figcaption id=\"caption-attachment-9411\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 4.\u00a0 Solu\u00e7\u00e3o Geral da Eq. 3<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Aplicando as condi\u00e7\u00f5es de contorno, apresentadas na Equa\u00e7\u00e3o 1, na Equa\u00e7\u00e3o 4, obtem-se a seguinte express\u00e3o:<\/span><\/p>\n<figure id=\"attachment_9412\" aria-describedby=\"caption-attachment-9412\" style=\"width: 515px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_6.png\"><img decoding=\"async\" class=\"size-full wp-image-9412\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_6.png\" alt=\"\" width=\"515\" height=\"51\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_6.png 515w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_6-300x30.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/a><figcaption id=\"caption-attachment-9412\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 5<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A solu\u00e7\u00e3o da Eq. 5 requer que <strong>B seja sempre igual a zero<\/strong> e:<\/span><\/p>\n<figure id=\"attachment_9413\" aria-describedby=\"caption-attachment-9413\" style=\"width: 537px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_7.png\"><img decoding=\"async\" class=\"wp-image-9413 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_7.png\" alt=\"\" width=\"537\" height=\"173\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_7.png 537w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_7-300x97.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/a><figcaption id=\"caption-attachment-9413\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 6<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 6 demonstra que existem n solu\u00e7\u00f5es dadas pela Equa\u00e7\u00e3o 7, e que n deve ser um n\u00famero inteiro maior do que zero. A constante A<sub>n<\/sub> pode ser um n\u00famero real ou complexo.<\/span><\/p>\n<figure id=\"attachment_9415\" aria-describedby=\"caption-attachment-9415\" style=\"width: 479px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_9.png\"><img decoding=\"async\" class=\"wp-image-9415 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_9.png\" alt=\"\" width=\"479\" height=\"78\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_9.png 479w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_9-300x49.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/a><figcaption id=\"caption-attachment-9415\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 7. Solu\u00e7\u00f5es da Eq. 3<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Substituindo a Equa\u00e7\u00e3o 7 na Equa\u00e7\u00e3o 3, obtem-se a energia cin\u00e9tica da part\u00edcula:<\/span><\/p>\n<figure id=\"attachment_9419\" aria-describedby=\"caption-attachment-9419\" style=\"width: 375px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/energia_caixa.png\"><img decoding=\"async\" class=\"size-full wp-image-9419\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/energia_caixa.png\" alt=\"\" width=\"375\" height=\"94\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/energia_caixa.png 375w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/energia_caixa-300x75.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/a><figcaption id=\"caption-attachment-9419\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 8. Energia da part\u00edcula na caixa[note] substituir hcortado por h Solymar e walsh[\/note]<\/figcaption><\/figure>\n<p class=\"p1\"><span style=\"font-family: verdana, geneva, sans-serif;\">A matem\u00e1tica revelou o comportamento qu\u00e2ntico da part\u00edcula. A Figura 2 mostra as n solu\u00e7\u00f5es poss\u00edveis com n\u00edveis de energia e fun\u00e7\u00f5es de onda distintos.<\/span><\/p>\n<figure id=\"attachment_9427\" aria-describedby=\"caption-attachment-9427\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa-1.png\"><img decoding=\"async\" class=\"wp-image-9427 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa-1.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa-1.png 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa-1-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa-1-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-9427\" class=\"wp-caption-text\">Figura 2. Fun\u00e7\u00f5es de Onda somadas \u00e0 Energia no caso de part\u00edcula na caixa<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Finalmente, resta normalizar as fun\u00e7\u00f5es de onda. Para isso precisamos calcular a integral do m\u00f3dulo da fun\u00e7\u00e3o de onda ao quadrado<span id='easy-footnote-3-9450' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/exemplo-particula-na-caixa\/#easy-footnote-bottom-3-9450\" title=\" eq.7\"><sup>3<\/sup><\/a><\/span> conforme a equa\u00e7\u00e3o abaixo:<\/span><\/p>\n<figure id=\"attachment_9425\" aria-describedby=\"caption-attachment-9425\" style=\"width: 767px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_11.png\"><img decoding=\"async\" class=\"size-full wp-image-9425\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_11.png\" alt=\"\" width=\"767\" height=\"346\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_11.png 767w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/na_caixa_11-300x135.png 300w\" sizes=\"(max-width: 767px) 100vw, 767px\" \/><\/a><figcaption id=\"caption-attachment-9425\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 9<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, a normaliza\u00e7\u00e3o requer que o valor das amplitudes da onda para que a integral da Equa\u00e7\u00e3o 9 seja unit\u00e1rio.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Finalmente, a Figura 3 apresenta o m\u00f3dulo da fun\u00e7\u00e3o de onda elevada ao quadrado e, neste caso, somada \u00e0 energia de cada n\u00edvel. Considerando que este gr\u00e1fico representa a probabilidade de localiza\u00e7\u00e3o da part\u00edcula dentro caixa, observamos que:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">a probabilidade \u00e9 m\u00ednima de encontrar el\u00e9trons nas bordas da caixa<span id='easy-footnote-4-9450' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/exemplo-particula-na-caixa\/#easy-footnote-bottom-4-9450\" title=\" Este resultado encontra-se de acordo com nosso senso comum\"><sup>4<\/sup><\/a><\/span>;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">a probabilidade de encontrar el\u00e9trons no centro da caixa \u00e9 m\u00e1xima apenas para n\u00fameros qu\u00e2nticos \u00edmpares;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Com o aumento do n\u00edvel energ\u00e9tico, surgem outros pontos de m\u00e1xima e de m\u00ednima probabilidade;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Para n\u00fameros qu\u00e2nticos pares o centro passa a apresentar probabilidade m\u00ednima e nos \u00edmpares m\u00e1ximas;<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<figure id=\"attachment_9429\" aria-describedby=\"caption-attachment-9429\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa_2.png\"><img decoding=\"async\" class=\"wp-image-9429 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa_2.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa_2.png 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa_2-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/particula_caixa_2-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-9429\" class=\"wp-caption-text\">Figura 3. M\u00f3dulo da fun\u00e7\u00e3o de onda somada \u00e0 energia no caso de part\u00edcula na caixa.<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este exemplo simples revelou aspectos importantes da mec\u00e2nica qu\u00e2ntica.<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><strong>A energia assume apenas um conjunto de valores discretos<\/strong>;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Existe <strong>um valor m\u00ednimo de energia para a part\u00edcula<\/strong>, superior ao valor m\u00ednimo do po\u00e7o;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O m\u00f3dulo da fun\u00e7\u00e3o de onda ao quadrado revela que <strong>a part\u00edcula n\u00e3o permanece uniformemente distribu\u00edda na caixa e que essa distribui\u00e7\u00e3o depende do n\u00famero qu\u00e2ntico e, consequentemente da energia<\/strong>.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><strong>Estes comportamentos inexistem se considerarmos a mec\u00e2nica cl\u00e1ssica<\/strong> aplicada a uma mesa de bilhar.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2 id='refer\u00eancias'  id=\"boomdevs_1\">Refer\u00eancias<\/h2>\n<ol>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">KREYSZIG, E. <strong>Advanced Engineering Mathematics<\/strong>, 9 edi\u00e7\u00e3o, John Wiley &amp; Sons, 2006.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">SOLYMAR, L., WALSH, D., Electrical Properties of Materials, Oxford, 2010.<\/span><\/li>\n<li style=\"text-align: left;\"><span style=\"font-family: verdana, geneva, sans-serif;\">MILLER, D.A.B, <strong>Quantum Mechanics for Scientists and Engineers<\/strong>, Cambridge University Press, 2008.<\/span><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>A maior dificuldade pr\u00e1tica da Equa\u00e7\u00e3o de Schr\u00f6dinger reside na dificuldade de resolu\u00e7\u00e3o de sistemas com muitas part\u00faiculas. Por isso, utilizam-se diversas simplifica\u00e7\u00f5es para analisar sistemas complexos. A part\u00edcula na caixa representa uma dessas simplifica\u00e7\u00f5es. Para visualizar melhor o significado e implica\u00e7\u00f5es da Equa\u00e7\u00e3o de Schr\u00f6dinger, considera-se o exemplo de uma part\u00edcula em movimento unidimensional [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":9203,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-9450","page","type-page","status-publish","has-post-thumbnail","hentry"],"uagb_featured_image_src":{"full":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/estrutura_mat-1.png",1200,280,false],"thumbnail":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/estrutura_mat-1-150x150.png",150,150,true],"medium":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/estrutura_mat-1-300x70.png",300,70,true],"medium_large":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/estrutura_mat-1-768x179.png",580,135,true],"large":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/estrutura_mat-1-1024x239.png",580,135,true],"1536x1536":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/estrutura_mat-1.png",1200,280,false],"2048x2048":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/estrutura_mat-1.png",1200,280,false],"post-thumbnail":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/estrutura_mat-1.png",1200,280,false],"twentytwenty-fullscreen":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/03\/estrutura_mat-1.png",1200,280,false]},"uagb_author_info":{"display_name":"admin","author_link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/author\/admin\/"},"uagb_comment_info":0,"uagb_excerpt":"A maior dificuldade pr\u00e1tica da Equa\u00e7\u00e3o de Schr\u00f6dinger reside na dificuldade de resolu\u00e7\u00e3o de sistemas com muitas part\u00faiculas. Por isso, utilizam-se diversas simplifica\u00e7\u00f5es para analisar sistemas complexos. A part\u00edcula na caixa representa uma dessas simplifica\u00e7\u00f5es. Para visualizar melhor o significado e implica\u00e7\u00f5es da Equa\u00e7\u00e3o de Schr\u00f6dinger, considera-se o exemplo de uma part\u00edcula em movimento unidimensional&hellip;","_links":{"self":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/9450","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/comments?post=9450"}],"version-history":[{"count":14,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/9450\/revisions"}],"predecessor-version":[{"id":44103,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/9450\/revisions\/44103"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/media\/9203"}],"wp:attachment":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/media?parent=9450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}