{"_buckets": {"deposit": "10d92bbd-5402-4586-b037-b312c79015fe"}, "_deposit": {"id": "40360", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "40360"}, "status": "published"}, "_oai": {"id": "oai:repository.dl.itc.u-tokyo.ac.jp:00040360"}, "item_4_biblio_info_7": {"attribute_name": "\u66f8\u8a8c\u60c5\u5831", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "1994", "bibliographicIssueDateType": "Issued"}, "bibliographicIssueNumber": "3", "bibliographicPageEnd": "615", "bibliographicPageStart": "589", "bibliographicVolumeNumber": "1", "bibliographic_titles": [{"bibliographic_title": "Journal of mathematical sciences, the University of Tokyo"}]}]}, "item_4_description_13": {"attribute_name": "\u30d5\u30a9\u30fc\u30de\u30c3\u30c8", "attribute_value_mlt": [{"subitem_description": "application/pdf", "subitem_description_type": "Other"}]}, "item_4_description_5": {"attribute_name": "\u6284\u9332", "attribute_value_mlt": [{"subitem_description": "In this paper, we study the behavior of eigenvalues and eigenfunctions of Schrodinger operators whose potentials have finitely many negative singularities. We prove that if potentials behave like $O(|x-p_i|^{-\u03c1})(0\u003c\u03c1\u003c2)$ near singular points $x=p_i$, then eigenvalues behave like $O(h^{-\\frac{2\u03c1}{2-\u03c1}})$ when the Planck constant $h$ approaches to zero. Then we obtain the asymptotic expansion of the eigenvalues and eigenfunctions in $h$. We also study the splitting of the lowest eigenvalues and show that the asymptotic is estimated by a suitable Riemann metric called Agmon distance.", "subitem_description_type": "Abstract"}]}, "item_4_publisher_20": {"attribute_name": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "Graduate School of Mathematical Sciences, The University of Tokyo"}]}, "item_4_source_id_10": {"attribute_name": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "attribute_value_mlt": [{"subitem_source_identifier": "AA11021653", "subitem_source_identifier_type": "NCID"}]}, "item_4_source_id_8": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "13405705", "subitem_source_identifier_type": "ISSN"}]}, "item_4_subject_15": {"attribute_name": "\u65e5\u672c\u5341\u9032\u5206\u985e\u6cd5", "attribute_value_mlt": [{"subitem_subject": "415", "subitem_subject_scheme": "NDC"}]}, "item_4_text_16": {"attribute_name": "Mathematical Reviews Number", "attribute_value_mlt": [{"subitem_text_value": "MR1322693"}]}, "item_4_text_17": {"attribute_name": "Mathmatical Subject Classification", "attribute_value_mlt": [{"subitem_text_value": "35Q40(MSC1991)"}, {"subitem_text_value": "35P20(MSC1991)"}]}, "item_4_text_33": {"attribute_name": "\u539f\u7a3f\u53d7\u9818\u65e5", "attribute_value_mlt": [{"subitem_text_value": "1994-01-20"}]}, "item_4_text_34": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"subitem_text_value": "Departmental Bulletin Paper"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Nakano, Fumihiko"}], "nameIdentifiers": [{"nameIdentifier": "138958", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2017-06-27"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "jms010305.pdf", "filesize": [{"value": "203.6 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 203600.0, "url": {"label": "jms010305.pdf", "url": "https://repository.dl.itc.u-tokyo.ac.jp/record/40360/files/jms010305.pdf"}, "version_id": "4e9d4138-0d27-4af1-8dbd-829c4552a5ca"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Semiclassical analysis of Schr\u00f6dinger operators with coulomb-like singular potentials", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Semiclassical analysis of Schr\u00f6dinger operators with coulomb-like singular potentials"}]}, "item_type_id": "4", "owner": "1", "path": ["312/6865/7071/7072", "9/504/6868/7073/7074"], "permalink_uri": "http://hdl.handle.net/2261/1573", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_value": "2008-03-04"}, "publish_date": "2008-03-04", "publish_status": "0", "recid": "40360", "relation": {}, "relation_version_is_last": true, "title": ["Semiclassical analysis of Schr\u00f6dinger operators with coulomb-like singular potentials"], "weko_shared_id": null}