{"title":"注自由粒子和谐振子Schrödinger方程的波前解集","authors":"Keiichi Kato, Masaharu Kobayashi, S. Ito","doi":"10.55937/sut/1328712681","DOIUrl":null,"url":null,"abstract":"In this paper, we determine the wave front sets of solutions to the Schrödinger equations of the Schrödinger evolution operator of a free particle and of a harmonic oscillator by using the representation of the Schrödinger evolution operator of a free particle introduced by Kato, Kobayashi and Ito (2011) and a new representation of the evolution operator of a harmonic oscillator via wave packet transform (short time Fourier transform). AMS 2010 Mathematics Subject Classification. 35Q41, 35A18.","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"31","resultStr":"{\"title\":\"Remark on wave front sets of solutions to Schrödinger equation of a free particle and a harmonic oscillator\",\"authors\":\"Keiichi Kato, Masaharu Kobayashi, S. Ito\",\"doi\":\"10.55937/sut/1328712681\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we determine the wave front sets of solutions to the Schrödinger equations of the Schrödinger evolution operator of a free particle and of a harmonic oscillator by using the representation of the Schrödinger evolution operator of a free particle introduced by Kato, Kobayashi and Ito (2011) and a new representation of the evolution operator of a harmonic oscillator via wave packet transform (short time Fourier transform). AMS 2010 Mathematics Subject Classification. 35Q41, 35A18.\",\"PeriodicalId\":38708,\"journal\":{\"name\":\"SUT Journal of Mathematics\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"31\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SUT Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55937/sut/1328712681\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SUT Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55937/sut/1328712681","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Remark on wave front sets of solutions to Schrödinger equation of a free particle and a harmonic oscillator
In this paper, we determine the wave front sets of solutions to the Schrödinger equations of the Schrödinger evolution operator of a free particle and of a harmonic oscillator by using the representation of the Schrödinger evolution operator of a free particle introduced by Kato, Kobayashi and Ito (2011) and a new representation of the evolution operator of a harmonic oscillator via wave packet transform (short time Fourier transform). AMS 2010 Mathematics Subject Classification. 35Q41, 35A18.
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