{"title":"扩展波包和量子到经典的转变","authors":"John S Briggs","doi":"10.1088/1361-6404/ad4f35","DOIUrl":null,"url":null,"abstract":"The standard description of the transition from quantum to classical mechanics presented in most text books is the proof that the quantum expectation values of position and momentum obey equations of Newtonian form. This is the Ehrenfest theorem. It is combined with the requirement that wave packets remain localised to describe a single particle moving according to classical mechanics. Hence, the natural spreading of wave packets is viewed as a quantum effect. In contradiction to this view, here it is argued that the spreading, where different momentum components separate, is the signature of the quantum to classical transition. The asymptotic spatial wave function becomes proportional to the initial momentum space wave function, which mirrors exactly the well-known far-field diffraction pattern in optics. Trajectories, defined as the locus of the normals to the expanding wave front, are used to illustrate the transition from quantum to classical motion. Again this is the analogue of the wave to beam transition in optics. It is suggested that this analysis of the quantum to classical transition should be incorporated routinely into introductory quantum mechanics courses.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Expanding wave packets and the quantum to classical transition\",\"authors\":\"John S Briggs\",\"doi\":\"10.1088/1361-6404/ad4f35\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The standard description of the transition from quantum to classical mechanics presented in most text books is the proof that the quantum expectation values of position and momentum obey equations of Newtonian form. This is the Ehrenfest theorem. It is combined with the requirement that wave packets remain localised to describe a single particle moving according to classical mechanics. Hence, the natural spreading of wave packets is viewed as a quantum effect. In contradiction to this view, here it is argued that the spreading, where different momentum components separate, is the signature of the quantum to classical transition. The asymptotic spatial wave function becomes proportional to the initial momentum space wave function, which mirrors exactly the well-known far-field diffraction pattern in optics. Trajectories, defined as the locus of the normals to the expanding wave front, are used to illustrate the transition from quantum to classical motion. Again this is the analogue of the wave to beam transition in optics. It is suggested that this analysis of the quantum to classical transition should be incorporated routinely into introductory quantum mechanics courses.\",\"PeriodicalId\":50480,\"journal\":{\"name\":\"European Journal of Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6404/ad4f35\",\"RegionNum\":4,\"RegionCategory\":\"教育学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"EDUCATION, SCIENTIFIC DISCIPLINES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1361-6404/ad4f35","RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"EDUCATION, SCIENTIFIC DISCIPLINES","Score":null,"Total":0}
Expanding wave packets and the quantum to classical transition
The standard description of the transition from quantum to classical mechanics presented in most text books is the proof that the quantum expectation values of position and momentum obey equations of Newtonian form. This is the Ehrenfest theorem. It is combined with the requirement that wave packets remain localised to describe a single particle moving according to classical mechanics. Hence, the natural spreading of wave packets is viewed as a quantum effect. In contradiction to this view, here it is argued that the spreading, where different momentum components separate, is the signature of the quantum to classical transition. The asymptotic spatial wave function becomes proportional to the initial momentum space wave function, which mirrors exactly the well-known far-field diffraction pattern in optics. Trajectories, defined as the locus of the normals to the expanding wave front, are used to illustrate the transition from quantum to classical motion. Again this is the analogue of the wave to beam transition in optics. It is suggested that this analysis of the quantum to classical transition should be incorporated routinely into introductory quantum mechanics courses.
期刊介绍:
European Journal of Physics is a journal of the European Physical Society and its primary mission is to assist in maintaining and improving the standard of taught physics in universities and other institutes of higher education.
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