{"id":294,"date":"2021-09-01T10:00:03","date_gmt":"2021-09-01T10:00:03","guid":{"rendered":"https:\/\/www.quantum-classical-physics.com\/qcp\/?p=294"},"modified":"2021-12-29T22:54:06","modified_gmt":"2021-12-29T22:54:06","slug":"hamilton-jacobi-approach-to-quantum-mechanics","status":"publish","type":"post","link":"https:\/\/www.quantum-classical-physics.com\/qcp\/hamilton-jacobi-approach-to-quantum-mechanics\/","title":{"rendered":"Hamilton-Jacobi approach to quantum mechanics"},"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>Negative kinetic energies can either be nonsense or convey a profound truth about the physical reality (e.g., antimatter in relativistic QED). In quantum mechanics, they are associated with some relevant manifestations (weak measurements, quantum backflow, Glauber quantum oscillator, etc.) and have been recently discovered in optics (optical backflow). Here, building on the analogy between optical waves and wave propagation of Hamilton-Jacobi (HJ) wave fronts, new effects caused by the Hamilton\u2019s principal function \u00a0&#8230; <a href=\"https:\/\/www.quantum-classical-physics.com\/qcp\/articles\/Hamilton-Jacobi-for-QM-representations_arXiv.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">read more<\/a><\/p>\n<h3><a href=\"https:\/\/www.quantum-classical-physics.com\/qcp\/articles\/Hamilton-Jacobi-for-QM-representations_arXiv.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Read the Abstract <\/a> (PDF)<\/h3>\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\/hamilton-jacobi-approach-to-quantum-mechanics\/\" class=\"more-link style1-button\">Read 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