{"title":"某些波型与利萨图之间的对应关系","authors":"K. Górska, A. Makowski, S. Dembinski","doi":"10.1088/0305-4470/39/42/006","DOIUrl":null,"url":null,"abstract":"We study the connections between some specially entangled stationary states and the classical periodic trajectories of two non-interacting oscillators. The latter are well-known Lissajous figures, which are shown to run precisely over the apogees of their corresponding probability distributions in the above states. We propose in this work a very simple criterion enabling us to obtain the best agreement between the quantum and the classical images. Finally, our results are successfully applied to the interpretation of some experimentally observed wave patterns.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Correspondence between some wave patterns and Lissajous figures\",\"authors\":\"K. Górska, A. Makowski, S. Dembinski\",\"doi\":\"10.1088/0305-4470/39/42/006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the connections between some specially entangled stationary states and the classical periodic trajectories of two non-interacting oscillators. The latter are well-known Lissajous figures, which are shown to run precisely over the apogees of their corresponding probability distributions in the above states. We propose in this work a very simple criterion enabling us to obtain the best agreement between the quantum and the classical images. Finally, our results are successfully applied to the interpretation of some experimentally observed wave patterns.\",\"PeriodicalId\":87442,\"journal\":{\"name\":\"Journal of physics A: Mathematical and general\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-10-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of physics A: Mathematical and general\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0305-4470/39/42/006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of physics A: Mathematical and general","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/39/42/006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Correspondence between some wave patterns and Lissajous figures
We study the connections between some specially entangled stationary states and the classical periodic trajectories of two non-interacting oscillators. The latter are well-known Lissajous figures, which are shown to run precisely over the apogees of their corresponding probability distributions in the above states. We propose in this work a very simple criterion enabling us to obtain the best agreement between the quantum and the classical images. Finally, our results are successfully applied to the interpretation of some experimentally observed wave patterns.