{"title":"Minimizing Schrödinger eigenvalues for confining potentials","authors":"Rupert L. Frank","doi":"arxiv-2407.15103","DOIUrl":null,"url":null,"abstract":"We consider the problem of minimizing the lowest eigenvalue of the\nSchr\\\"odinger operator $-\\Delta+V$ in $L^2(\\mathbb R^d)$ when the integral\n$\\int e^{-tV}\\,dx$ is given for some $t>0$. We show that the eigenvalue is\nminimal for the harmonic oscillator and derive a quantitative version of the\ncorresponding inequality.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.15103","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the problem of minimizing the lowest eigenvalue of the
Schr\"odinger operator $-\Delta+V$ in $L^2(\mathbb R^d)$ when the integral
$\int e^{-tV}\,dx$ is given for some $t>0$. We show that the eigenvalue is
minimal for the harmonic oscillator and derive a quantitative version of the
corresponding inequality.
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
