{"id":910,"date":"2015-11-30T15:48:48","date_gmt":"2015-11-30T15:48:48","guid":{"rendered":"http:\/\/quant-math.org\/wp\/?p=910"},"modified":"2015-12-20T16:03:44","modified_gmt":"2015-12-20T16:03:44","slug":"particle-detection-and-non-detection-in-a-quantum-time-of-arrival-measurement-d-sombillo-and-e-a-galapon","status":"publish","type":"post","link":"https:\/\/quant-math.org\/wp\/2015\/11\/30\/particle-detection-and-non-detection-in-a-quantum-time-of-arrival-measurement-d-sombillo-and-e-a-galapon\/","title":{"rendered":"Particle detection and non-detection in a quantum time of arrival measurement (D. Sombillo and E.A. Galapon, Annals of Physics, 364,  261\u2013273 (2016))"},"content":{"rendered":"<h3>Abstract<\/h3>\n<blockquote><p> The standard time-of-arrival distribution cannot reproduce both the temporal and the spatial profile of the modulus squared of the time-evolved wave function for an arbitrary initial state. In particular, the time-of-arrival distribution gives a non-vanishing probability even if the wave function is zero at a given point for all values of time. This poses a problem in the standard formulation of quantum mechanics where one quantizes a classical observable and uses its spectral resolution to calculate the corresponding distribution. In this work, we show that the modulus square of the time-evolved wave function is in fact contained in one of the degenerate eigenfunctions of the quantized time-of-arrival operator. This generalizes our understanding of quantum arrival phenomenon where particle detection is not a necessary requirement, thereby providing a direct link between time-of-arrival quantization and the outcomes of the two-slit experiment.<\/p><\/blockquote>\n<p>In press, Annals of Physics (2015). The free online and pdf version is <a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S000349161500411X\" target=\"_blank\">here<\/a>, free until 24 January 2016. The preprint is <a href=\"http:\/\/quant-math.org\/uploads\/preprints\/SombilloGalaponAOP.pdf\" target=\"_blank\">here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Abstract The standard time-of-arrival distribution cannot reproduce both the temporal and the spatial profile of the modulus squared of the time-evolved wave function for an arbitrary initial state. In particular, the time-of-arrival distribution gives a non-vanishing probability even if the wave function is zero at a given point for all values of time. This poses\u2026 <span class=\"read-more\"><a href=\"https:\/\/quant-math.org\/wp\/2015\/11\/30\/particle-detection-and-non-detection-in-a-quantum-time-of-arrival-measurement-d-sombillo-and-e-a-galapon\/\">Read More: Particle detection and non-detection in a quantum time of arrival\u2026 &raquo;<\/a><\/span><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-910","post","type-post","status-publish","format-standard","hentry","category-preprints"],"_links":{"self":[{"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/posts\/910","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/comments?post=910"}],"version-history":[{"count":10,"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/posts\/910\/revisions"}],"predecessor-version":[{"id":921,"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/posts\/910\/revisions\/921"}],"wp:attachment":[{"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/media?parent=910"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/categories?post=910"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quant-math.org\/wp\/wp-json\/wp\/v2\/tags?post=910"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}