{"id":316,"date":"2023-01-23T11:21:12","date_gmt":"2023-01-23T11:21:12","guid":{"rendered":"https:\/\/www.quantum-classical-physics.com\/qcp\/?p=316"},"modified":"2023-01-28T19:42:18","modified_gmt":"2023-01-28T19:42:18","slug":"a-call-to-action-schrodingers-representation-of-quantum-mechanics-via-hamiltons-principle","status":"publish","type":"post","link":"https:\/\/www.quantum-classical-physics.com\/qcp\/a-call-to-action-schrodingers-representation-of-quantum-mechanics-via-hamiltons-principle\/","title":{"rendered":"\u201cA call to action\u201d: Schr\u00f6dinger\u2019s representation of quantum mechanics via Hamilton\u2019s principle"},"content":{"rendered":"<div  class=\"tatsu-g7apowtr2v7qcctc tatsu-section  tatsu-bg-overlay   tatsu-clearfix\" data-title=\"\"  data-headerscheme=\"background--dark\"><div class='tatsu-section-pad clearfix' data-padding='{\"d\":\"15px 0px 15px 0px\"}' data-padding-top='15px'><div class=\"tatsu-row-wrap  tatsu-wrap tatsu-row-one-col tatsu-row-has-one-cols tatsu-medium-gutter tatsu-reg-cols  tatsu-clearfix tatsu-g7apowtr987vhqoh\" ><div  class=\"tatsu-row \" ><div  class=\"tatsu-column  tatsu-bg-overlay tatsu-one-col tatsu-column-image-none tatsu-column-effect-none  tatsu-g7apowtrdra9kr51\"  data-parallax-speed=\"0\" style=\"\"><div class=\"tatsu-column-inner \" ><div class=\"tatsu-column-pad-wrap\"><div class=\"tatsu-column-pad\" ><div  class=\"tatsu-module tatsu-text-block-wrap tatsu-g7apowtrhlabwa9h  \"><div class=\"tatsu-text-inner tatsu-align-center  clearfix\" ><style>.tatsu-g7apowtrhlabwa9h.tatsu-text-block-wrap .tatsu-text-inner{width: 100%;text-align: left;}<\/style>\n<p><span style=\"color: #ffffff; font-size: 8pt;\">Simple derivation of Schr\u00f6dinger equation from Newtonian dynamics<\/span> Michele Marrocco Dipartimento di Fisica, Universit\u00e0 di Roma \u2018La Sapienza\u2019 P.le Aldo Moro 5, I-00185 Rome, Italy &amp; ENEA (Italian National Agency for New Technologies, Energies and Sustainable Economic Development) via Anguillarese 301, I-00123 Rome, Italy<\/p>\n<h3>Abstract<\/h3>\n<p><span style=\"font-size: 14pt;\">A few years ago, one of the former Editors of this journal launched \u201ca call to action\u201d (E. F.\u00a0<\/span><span style=\"font-size: 14pt;\">Taylor, Am. J. Phys. 71, 423 (2003)) for a revision of teaching methods in physics in order to<\/span>\u00a0<span style=\"font-size: 14pt;\">emphasize the importance of the principle of least action. In response, we suggest the use of\u00a0<\/span><span style=\"font-size: 14pt;\">Hamilton\u2019s principle of stationary action to introduce the Schr\u00f6dinger equation. When\u00a0<\/span><span style=\"font-size: 14pt;\">considering the geometric interpretation of Hamilton-Jacobi theory, the real part of the action<\/span>\u00a0<span style=\"font-size: 14pt;\">\ud835\udc46 defines the phase of the wave function \ud835\udc52\ud835\udc65\ud835\udc5d(\ud835\udc56\ud835\udc46\/\u210f) and requiring the Hamilton-Jacobi wave\u00a0<\/span><span style=\"font-size: 14pt;\">function to obey wave-front propagation (i.e., Re(\ud835\udc46) is a constant of the motion) yields the\u00a0<\/span><span style=\"font-size: 14pt;\">Schr\u00f6dinger equation&#8230;<\/span><\/p>\n<h5 style=\"text-align: center;\">This article may be downloaded for personal use only.<br \/>Any other use requires prior permission of the author and AIP Publishing.\u00a0This article appeared in<br \/>American Journal of Physics and may be found at\u00a0<a href=\"https:\/\/aapt.scitation.org\/doi\/10.1119\/5.0083015\" target=\"_blank\" rel=\"noopener noreferrer\"> DOI: 10.1119\/5.0083015<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.quantum-classical-physics.com\/qcp\/articles\/AJP21-AR-01068.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Full Text (PDF)<\/a><\/h5>\n<\/div><\/div><\/div><\/div><div class = \"tatsu-column-bg-image-wrap\"><div class = \"tatsu-column-bg-image\" ><\/div><\/div><div class=\"tatsu-overlay tatsu-column-overlay tatsu-animate-none\" ><\/div><\/div><style>.tatsu-row > .tatsu-g7apowtrdra9kr51.tatsu-column{width: 100%;}.tatsu-g7apowtrdra9kr51.tatsu-column > .tatsu-column-inner > .tatsu-column-overlay{mix-blend-mode: normal;}.tatsu-g7apowtrdra9kr51 > .tatsu-column-inner > .tatsu-top-divider{z-index: 9999;}.tatsu-g7apowtrdra9kr51 > .tatsu-column-inner > .tatsu-bottom-divider{z-index: 9999;}.tatsu-g7apowtrdra9kr51 > .tatsu-column-inner > .tatsu-left-divider{z-index: 9999;}.tatsu-g7apowtrdra9kr51 > .tatsu-column-inner > .tatsu-right-divider{z-index: 9999;}<\/style><\/div><\/div><\/div><\/div><div class=\"tatsu-section-background-wrap\"><div class = \"tatsu-section-background\" ><\/div><\/div><div class=\"tatsu-overlay tatsu-section-overlay\"><\/div><style>.tatsu-g7apowtr2v7qcctc .tatsu-section-pad{padding: 15px 0px 15px 0px;}.tatsu-g7apowtr2v7qcctc > .tatsu-bottom-divider{z-index: 9999;}.tatsu-g7apowtr2v7qcctc > .tatsu-top-divider{z-index: 9999;}.tatsu-g7apowtr2v7qcctc .tatsu-section-overlay{mix-blend-mode: normal;}<\/style><\/div>\n","protected":false},"excerpt":{"rendered":"<p><a href=\"https:\/\/www.quantum-classical-physics.com\/qcp\/a-call-to-action-schrodingers-representation-of-quantum-mechanics-via-hamiltons-principle\/\" class=\"more-link style1-button\">Read More<\/a><\/p>","protected":false},"author":1,"featured_media":330,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>&quot;A call to action&quot;: Schr\u00f6dinger&#039;s representation of quantum...<\/title>\n<meta name=\"description\" content=\"A few years ago, one of the former Editors of this journal launched \u201ca call to action\u201d (E. F.Taylor, Am. J. Phys. 71, 423 (2003)...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.quantum-classical-physics.com\/qcp\/a-call-to-action-schrodingers-representation-of-quantum-mechanics-via-hamiltons-principle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"&quot;A call to action&quot;: Schr\u00f6dinger&#039;s representation of quantum...\" \/>\n<meta property=\"og:description\" content=\"A few years ago, one of the former Editors of this journal launched \u201ca call to action\u201d (E. F.Taylor, Am. J. 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