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Here we present the explicit forms of infinitely many seed solutions for adding eigenstates at arbitrary real energy through the Abraham-Moses transformations for typical solvable potentials, e.g., the radial oscillator, the Darboux-Poschl-Teller, and some others. These seed solutions are simple generalisations of the virtual state wavefunctions, which are obtained from the eigenfunctions by discrete symmetries of the potentials. The virtual state wavefunctions have been an essential ingredient for constructing multi-indexed Laguerre and Jacobi polynomials through multiple Darboux-Crum transformations. 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Here we present the explicit forms of infinitely many seed solutions for adding eigenstates at arbitrary real energy through the Abraham-Moses transformations for typical solvable potentials, e.g., the radial oscillator, the Darboux-Poschl-Teller, and some others. These seed solutions are simple generalisations of the virtual state wavefunctions, which are obtained from the eigenfunctions by discrete symmetries of the potentials. The virtual state wavefunctions have been an essential ingredient for constructing multi-indexed Laguerre and Jacobi polynomials through multiple Darboux-Crum transformations. In contrast to the Darboux transformations, the virtual state wavefunctions generate non-polynomial extensions of solvable potentials through the Abraham-Moses transformations. \u00a9 2013 AIP Publishing LLC."}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Odake,  Satoru"}], "nameIdentifiers": [{"nameIdentifier": "35915", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "Sasaki,  Ryu"}], "nameIdentifiers": [{"nameIdentifier": "35916", "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": "2015-09-28"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "Non-polynomial_extensions_solvable_potentials.pdf", "filesize": [{"value": "282.1 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_note", "mimetype": "application/pdf", "size": 282100.0, "url": {"label": "Non-polynomial_extensions_solvable_potentials.pdf", "url": "https://soar-ir.repo.nii.ac.jp/record/11716/files/Non-polynomial_extensions_solvable_potentials.pdf"}, "version_id": "e2e2c381-752a-42fa-b007-67d9edf2fbd6"}]}, "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": "journal article", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Non-polynomial extensions of solvable potentials a la Abraham-Moses", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Non-polynomial extensions of solvable potentials a la Abraham-Moses", "subitem_title_language": "en"}]}, "item_type_id": "6", "owner": "1", "path": ["1169/1170"], "permalink_uri": "http://hdl.handle.net/10091/17868", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2014-09-05"}, "publish_date": "2014-09-05", "publish_status": "0", "recid": "11716", "relation": {}, "relation_version_is_last": true, "title": ["Non-polynomial extensions of solvable potentials a la Abraham-Moses"], "weko_shared_id": -1}