{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:48:22Z","timestamp":1777448902912,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2011,7,1]],"date-time":"2011-07-01T00:00:00Z","timestamp":1309478400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2011,7]]},"abstract":"<jats:p>We study non-linear ground states of the Gross\u2013Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential. The Thomas\u2013Fermi approximation of ground states on various spatial scales was recently justified using variational methods. We justify here the Thomas\u2013Fermi approximation on an uniform spatial scale using the Painlev\u00e9-II equation. In the space of one dimension, these results allow us to characterize the distribution of eigenvalues in the point spectrum of the Schr\u00f6dinger operator associated with the non-linear ground state.<\/jats:p>","DOI":"10.3233\/asy-2011-1034","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:16:49Z","timestamp":1575055009000},"page":"53-96","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":12,"title":["On the Thomas\u2013Fermi ground state in a harmonic potential"],"prefix":"10.1177","volume":"73","author":[{"given":"Cl\u00e9ment","family":"Gallo","sequence":"first","affiliation":[{"name":"Institut de Math\u00e9matiques et de Mod\u00e9lisation de Montpellier, Universit\u00e9 Montpellier II, 34095 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry","family":"Pelinovsky","sequence":"additional","affiliation":[{"name":"Department of Mathematics, McMaster University, Hamilton, ON L8S 4K1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2011,7,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1034","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1034","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:20Z","timestamp":1777379960000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2011-1034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2011,7]]}},"alternative-id":["10.3233\/ASY-2011-1034"],"URL":"https:\/\/doi.org\/10.3233\/asy-2011-1034","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7]]}}}