{"id":{"repo_id":"bradford","oai_identifier":"oai:bradscholars.brad.ac.uk:10454/4895"},"canonical_url":"https://search.dev.ndltd.org/etd/bradford/oai:bradscholars.brad.ac.uk:10454/4895","repository":{"repo_id":"bradford","name":"University of Bradford","base_url":"https://bradscholars.brad.ac.uk/oai/request"},"display":{"title":"Schrödinger equation with periodic potentials.","abstract":"The Schrödinger equation ... is considered. The solution of this equation is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the eigenvalues is shown. The eigenvectors of the multiwells potential are presented. The solutions of Schrödinger equation are calculated. The results are very sensitive to the value of the parameter y. Localized solutions, in the case that the energy is slightly greater than the maximum value of the potential, are presented. Wigner and Weyl functions, corresponding to the solutions of Schrödinger equation, are also studied. It is also shown that they are very sensitive to the value of the parameter y.","abstract_html":"The Schrödinger equation ... is considered. The solution of this equation is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the eigenvalues is shown. The eigenvectors of the multiwells potential are presented. The solutions of Schrödinger equation are calculated. The results are very sensitive to the value of the parameter y. Localized solutions, in the case that the energy is slightly greater than the maximum value of the potential, are presented. Wigner and Weyl functions, corresponding to the solutions of Schrödinger equation, are also studied. It is also shown that they are very sensitive to the value of the parameter y.","abstract_has_math":false,"creators":["Mugassabi, Souad"],"institution":"University of Bradford","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Vourdas, Apostolos"],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-27","date_published":"2011-05-27","updated_at":"2026-07-24T01:15:08Z","subjects":["Schrödinger equation","Eigenvectors","Weyl function","Wigner function"],"languages":["en"],"rights":["<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png\" /></a><br />The University of Bradford theses are licenced under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\">Creative Commons Licence</a>."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10454/4895","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Vourdas, Apostolos"]},{"key":"dc:creator","label":"Author","values":["Mugassabi, Souad"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2011-05-27T15:49:28Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-05-27T15:49:28Z"]},{"key":"dc:date.issued","label":"Date","values":["2011-05-27"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Bradford"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Schrödinger equation","Eigenvectors","Weyl function","Wigner function"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png\" /></a><br />The University of Bradford theses are licenced under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\">Creative Commons Licence</a>."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10454/4895"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Schrödinger equation ... is considered. The solution of this equation is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the eigenvalues is shown. The eigenvectors of the multiwells potential are presented. The solutions of Schrödinger equation are calculated. The results are very sensitive to the value of the parameter y. Localized solutions, in the case that the energy is slightly greater than the maximum value of the potential, are presented. Wigner and Weyl functions, corresponding to the solutions of Schrödinger equation, are also studied. It is also shown that they are very sensitive to the value of the parameter y."]},{"key":"dc:title","label":"Title","values":["Schrödinger equation with periodic potentials."]}]}],"canonical_facts":{"dc:contributor.advisor":["Vourdas, Apostolos"],"dc:creator":["Mugassabi, Souad"],"dc:date.accessioned":["2011-05-27T15:49:28Z"],"dc:date.available":["2011-05-27T15:49:28Z"],"dc:date.issued":["2011-05-27"],"dc:description.abstract":["The Schrödinger equation ... is considered. The solution of this equation is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the eigenvalues is shown. The eigenvectors of the multiwells potential are presented. The solutions of Schrödinger equation are calculated. The results are very sensitive to the value of the parameter y. Localized solutions, in the case that the energy is slightly greater than the maximum value of the potential, are presented. Wigner and Weyl functions, corresponding to the solutions of Schrödinger equation, are also studied. It is also shown that they are very sensitive to the value of the parameter y."],"dc:identifier.uri":["http://hdl.handle.net/10454/4895"],"dc:language.iso":["en"],"dc:publisher.department":["Department of Mathematics"],"dc:publisher.institution":["University of Bradford"],"dc:rights":["<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png\" /></a><br />The University of Bradford theses are licenced under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\">Creative Commons Licence</a>."],"dc:subject":["Schrödinger equation","Eigenvectors","Weyl function","Wigner function"],"dc:title":["Schrödinger equation with periodic potentials."],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-24T01:15:08Z"}