Loading…
Intertwined isospectral potentials in an arbitrary dimension
The method of intertwining with n-dimensional (n D ) linear intertwining operator L is used to construct n D isospectral, stationary potentials. It has been proven that the differential part of L is a series in Euclidean algebra generators. Integrability conditions of the consistency equations are i...
Saved in:
Published in: | Journal of mathematical physics 2001-08, Vol.42 (8), p.3344-3360 |
---|---|
Main Authors: | , , |
Format: | Article |
Language: | English |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
cited_by | cdi_FETCH-LOGICAL-c363t-39672563b8fd275d058f584a2a79379a04a69d534e08f0816597e7954aca93093 |
---|---|
cites | cdi_FETCH-LOGICAL-c363t-39672563b8fd275d058f584a2a79379a04a69d534e08f0816597e7954aca93093 |
container_end_page | 3360 |
container_issue | 8 |
container_start_page | 3344 |
container_title | Journal of mathematical physics |
container_volume | 42 |
creator | Kuru, Ş. Teğmen, A. Verçin, A. |
description | The method of intertwining with n-dimensional
(n
D
)
linear intertwining operator
L
is used to construct
n
D
isospectral, stationary potentials. It has been proven that the differential part of
L
is a series in Euclidean algebra generators. Integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each
n=2, 3, 4, 5.
The most general forms of 2D and 3D isospectral potentials are considered in detail and construction of their hierarchies is exhibited. The followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1D systems. It has been shown that in choice of coordinates and
L
there are a number of alternatives increasing with n that enlarge the set of available potentials. Some salient features of higher dimensional extension as well as some applications of the results are presented. |
doi_str_mv | 10.1063/1.1383787 |
format | article |
fullrecord | <record><control><sourceid>scitation_cross</sourceid><recordid>TN_cdi_scitation_primary_10_1063_1_1383787</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>jmp</sourcerecordid><originalsourceid>FETCH-LOGICAL-c363t-39672563b8fd275d058f584a2a79379a04a69d534e08f0816597e7954aca93093</originalsourceid><addsrcrecordid>eNp9z01LAzEQBuAgCtbqwX-wV4Wtk-8EvEjxo1DwoueQbhKItNklCYr_3kiLHgRhYA7z8DIvQpcYFhgEvcELTBWVSh6hGQaleym4OkYzAEJ6wpQ6RWelvAFgrBibodtVqj7Xj5i862IZy-SHmu22m8bqU412W7qYOtsmb2K75M_OxZ1PJY7pHJ2EBvzFYc_R68P9y_KpXz8_rpZ3636ggtaeaiEJF3SjgiOSO-AqcMUssVJTqS0wK7TjlHlQARQWXEsvNWd2sJqCpnN0tc8d8lhK9sFMOe7aKwaD-a5tsDnUbvZ6b8sQq63tyx_8PuZfaCYX_sN_k78AxvVlcg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Intertwined isospectral potentials in an arbitrary dimension</title><source>American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list)</source><source>American Institute of Physics</source><creator>Kuru, Ş. ; Teğmen, A. ; Verçin, A.</creator><creatorcontrib>Kuru, Ş. ; Teğmen, A. ; Verçin, A.</creatorcontrib><description>The method of intertwining with n-dimensional
(n
D
)
linear intertwining operator
L
is used to construct
n
D
isospectral, stationary potentials. It has been proven that the differential part of
L
is a series in Euclidean algebra generators. Integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each
n=2, 3, 4, 5.
The most general forms of 2D and 3D isospectral potentials are considered in detail and construction of their hierarchies is exhibited. The followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1D systems. It has been shown that in choice of coordinates and
L
there are a number of alternatives increasing with n that enlarge the set of available potentials. Some salient features of higher dimensional extension as well as some applications of the results are presented.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.1383787</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><ispartof>Journal of mathematical physics, 2001-08, Vol.42 (8), p.3344-3360</ispartof><rights>American Institute of Physics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-39672563b8fd275d058f584a2a79379a04a69d534e08f0816597e7954aca93093</citedby><cites>FETCH-LOGICAL-c363t-39672563b8fd275d058f584a2a79379a04a69d534e08f0816597e7954aca93093</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.1383787$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,782,784,795,27924,27925,76383</link.rule.ids></links><search><creatorcontrib>Kuru, Ş.</creatorcontrib><creatorcontrib>Teğmen, A.</creatorcontrib><creatorcontrib>Verçin, A.</creatorcontrib><title>Intertwined isospectral potentials in an arbitrary dimension</title><title>Journal of mathematical physics</title><description>The method of intertwining with n-dimensional
(n
D
)
linear intertwining operator
L
is used to construct
n
D
isospectral, stationary potentials. It has been proven that the differential part of
L
is a series in Euclidean algebra generators. Integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each
n=2, 3, 4, 5.
The most general forms of 2D and 3D isospectral potentials are considered in detail and construction of their hierarchies is exhibited. The followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1D systems. It has been shown that in choice of coordinates and
L
there are a number of alternatives increasing with n that enlarge the set of available potentials. Some salient features of higher dimensional extension as well as some applications of the results are presented.</description><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNp9z01LAzEQBuAgCtbqwX-wV4Wtk-8EvEjxo1DwoueQbhKItNklCYr_3kiLHgRhYA7z8DIvQpcYFhgEvcELTBWVSh6hGQaleym4OkYzAEJ6wpQ6RWelvAFgrBibodtVqj7Xj5i862IZy-SHmu22m8bqU412W7qYOtsmb2K75M_OxZ1PJY7pHJ2EBvzFYc_R68P9y_KpXz8_rpZ3636ggtaeaiEJF3SjgiOSO-AqcMUssVJTqS0wK7TjlHlQARQWXEsvNWd2sJqCpnN0tc8d8lhK9sFMOe7aKwaD-a5tsDnUbvZ6b8sQq63tyx_8PuZfaCYX_sN_k78AxvVlcg</recordid><startdate>200108</startdate><enddate>200108</enddate><creator>Kuru, Ş.</creator><creator>Teğmen, A.</creator><creator>Verçin, A.</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>200108</creationdate><title>Intertwined isospectral potentials in an arbitrary dimension</title><author>Kuru, Ş. ; Teğmen, A. ; Verçin, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-39672563b8fd275d058f584a2a79379a04a69d534e08f0816597e7954aca93093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kuru, Ş.</creatorcontrib><creatorcontrib>Teğmen, A.</creatorcontrib><creatorcontrib>Verçin, A.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kuru, Ş.</au><au>Teğmen, A.</au><au>Verçin, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Intertwined isospectral potentials in an arbitrary dimension</atitle><jtitle>Journal of mathematical physics</jtitle><date>2001-08</date><risdate>2001</risdate><volume>42</volume><issue>8</issue><spage>3344</spage><epage>3360</epage><pages>3344-3360</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>The method of intertwining with n-dimensional
(n
D
)
linear intertwining operator
L
is used to construct
n
D
isospectral, stationary potentials. It has been proven that the differential part of
L
is a series in Euclidean algebra generators. Integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each
n=2, 3, 4, 5.
The most general forms of 2D and 3D isospectral potentials are considered in detail and construction of their hierarchies is exhibited. The followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1D systems. It has been shown that in choice of coordinates and
L
there are a number of alternatives increasing with n that enlarge the set of available potentials. Some salient features of higher dimensional extension as well as some applications of the results are presented.</abstract><doi>10.1063/1.1383787</doi><tpages>17</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0022-2488 |
ispartof | Journal of mathematical physics, 2001-08, Vol.42 (8), p.3344-3360 |
issn | 0022-2488 1089-7658 |
language | eng |
recordid | cdi_scitation_primary_10_1063_1_1383787 |
source | American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list); American Institute of Physics |
title | Intertwined isospectral potentials in an arbitrary dimension |
url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T12%3A10%3A10IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-scitation_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Intertwined%20isospectral%20potentials%20in%20an%20arbitrary%20dimension&rft.jtitle=Journal%20of%20mathematical%20physics&rft.au=Kuru,%20%C5%9E.&rft.date=2001-08&rft.volume=42&rft.issue=8&rft.spage=3344&rft.epage=3360&rft.pages=3344-3360&rft.issn=0022-2488&rft.eissn=1089-7658&rft.coden=JMAPAQ&rft_id=info:doi/10.1063/1.1383787&rft_dat=%3Cscitation_cross%3Ejmp%3C/scitation_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c363t-39672563b8fd275d058f584a2a79379a04a69d534e08f0816597e7954aca93093%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |