{"title":"环状Stokes曲线Schrödinger方程的精确WKB分析","authors":"T. Aoki, Kohei Iwaki, Toshinori Takahashi","doi":"10.1619/FESI.62.1","DOIUrl":null,"url":null,"abstract":"Stokes phenomena with respect to a large parameter are investigated for Shrödinger-type ordinary di¤erential equations having a Stokes curve of loop-type. For this purpose, we employ a Bessel-type equation as a canonical form and compute the Voros coe‰cient of the equation. Combining the formula describing the Stokes automorphism for the Voros coe‰cient and the formal coordinate transformation connecting the Shrödinger-type equation and the Bessel-type equation, we have some formulas describing the action of alien derivatives and Stokes automorphism for WKB solutions of the Shrödinger-type equation.","PeriodicalId":55134,"journal":{"name":"Funkcialaj Ekvacioj-Serio Internacia","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1619/FESI.62.1","citationCount":"13","resultStr":"{\"title\":\"Exact WKB Analysis of Schrödinger Equations with a Stokes Curve of Loop Type\",\"authors\":\"T. Aoki, Kohei Iwaki, Toshinori Takahashi\",\"doi\":\"10.1619/FESI.62.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Stokes phenomena with respect to a large parameter are investigated for Shrödinger-type ordinary di¤erential equations having a Stokes curve of loop-type. For this purpose, we employ a Bessel-type equation as a canonical form and compute the Voros coe‰cient of the equation. Combining the formula describing the Stokes automorphism for the Voros coe‰cient and the formal coordinate transformation connecting the Shrödinger-type equation and the Bessel-type equation, we have some formulas describing the action of alien derivatives and Stokes automorphism for WKB solutions of the Shrödinger-type equation.\",\"PeriodicalId\":55134,\"journal\":{\"name\":\"Funkcialaj Ekvacioj-Serio Internacia\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1619/FESI.62.1\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Funkcialaj Ekvacioj-Serio Internacia\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1619/FESI.62.1\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Funkcialaj Ekvacioj-Serio Internacia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1619/FESI.62.1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Exact WKB Analysis of Schrödinger Equations with a Stokes Curve of Loop Type
Stokes phenomena with respect to a large parameter are investigated for Shrödinger-type ordinary di¤erential equations having a Stokes curve of loop-type. For this purpose, we employ a Bessel-type equation as a canonical form and compute the Voros coe‰cient of the equation. Combining the formula describing the Stokes automorphism for the Voros coe‰cient and the formal coordinate transformation connecting the Shrödinger-type equation and the Bessel-type equation, we have some formulas describing the action of alien derivatives and Stokes automorphism for WKB solutions of the Shrödinger-type equation.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
