Integrals of motion and quantum operators for hydrogenic atoms in external fields

Detalhes bibliográficos
Autor(a) principal: Beims, Marcus Werner
Data de Publicação: 2000
Outros Autores: Gallas, Jason Alfredo Carlson
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/104173
Resumo: We report five cases of integrability for a hydrogenic atom under three static external fields: a magnetic field, an electric field, and a van der Waals interaction. Exact integrals of motion and corresponding quantum operators are obtained explicitly for each case. Integrals of motion (quantum operators) can be expressed as components of a suitably generalized Runge-Lenz vector (operator). Quadratic quantum operators are found to have the amazing property of requiring a nonclassical extra term proportional to h². The structuring of the classical phase space is investigated numerically via Poincare surfaces of section and corroborates the analytical results.
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spelling Beims, Marcus WernerGallas, Jason Alfredo Carlson2014-10-04T02:13:29Z20001050-2947http://hdl.handle.net/10183/104173000275818We report five cases of integrability for a hydrogenic atom under three static external fields: a magnetic field, an electric field, and a van der Waals interaction. Exact integrals of motion and corresponding quantum operators are obtained explicitly for each case. Integrals of motion (quantum operators) can be expressed as components of a suitably generalized Runge-Lenz vector (operator). Quadratic quantum operators are found to have the amazing property of requiring a nonclassical extra term proportional to h². The structuring of the classical phase space is investigated numerically via Poincare surfaces of section and corroborates the analytical results.application/pdfengPhysical review. A, Atomic, molecular, and optical physics. New York. Vol. 62, no. 4 (Oct. 2000), 043410 12p.Teoria quânticaIntegrals of motion and quantum operators for hydrogenic atoms in external fieldsEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000275818.pdf000275818.pdfTexto completo (inglês)application/pdf245219http://www.lume.ufrgs.br/bitstream/10183/104173/1/000275818.pdfd312949b0587037d2abda96e8fba4631MD51TEXT000275818.pdf.txt000275818.pdf.txtExtracted Texttext/plain45052http://www.lume.ufrgs.br/bitstream/10183/104173/2/000275818.pdf.txte872c30b9035362dab85e015ee8dd1f6MD52THUMBNAIL000275818.pdf.jpg000275818.pdf.jpgGenerated Thumbnailimage/jpeg1956http://www.lume.ufrgs.br/bitstream/10183/104173/3/000275818.pdf.jpg058ef9b0dadc780af9e0f6892f71fce9MD5310183/1041732024-03-28 06:23:59.96922oai:www.lume.ufrgs.br:10183/104173Repositório InstitucionalPUBhttps://lume.ufrgs.br/oai/requestlume@ufrgs.bropendoar:2024-03-28T09:23:59Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Integrals of motion and quantum operators for hydrogenic atoms in external fields
title Integrals of motion and quantum operators for hydrogenic atoms in external fields
spellingShingle Integrals of motion and quantum operators for hydrogenic atoms in external fields
Beims, Marcus Werner
Teoria quântica
title_short Integrals of motion and quantum operators for hydrogenic atoms in external fields
title_full Integrals of motion and quantum operators for hydrogenic atoms in external fields
title_fullStr Integrals of motion and quantum operators for hydrogenic atoms in external fields
title_full_unstemmed Integrals of motion and quantum operators for hydrogenic atoms in external fields
title_sort Integrals of motion and quantum operators for hydrogenic atoms in external fields
author Beims, Marcus Werner
author_facet Beims, Marcus Werner
Gallas, Jason Alfredo Carlson
author_role author
author2 Gallas, Jason Alfredo Carlson
author2_role author
dc.contributor.author.fl_str_mv Beims, Marcus Werner
Gallas, Jason Alfredo Carlson
dc.subject.por.fl_str_mv Teoria quântica
topic Teoria quântica
description We report five cases of integrability for a hydrogenic atom under three static external fields: a magnetic field, an electric field, and a van der Waals interaction. Exact integrals of motion and corresponding quantum operators are obtained explicitly for each case. Integrals of motion (quantum operators) can be expressed as components of a suitably generalized Runge-Lenz vector (operator). Quadratic quantum operators are found to have the amazing property of requiring a nonclassical extra term proportional to h². The structuring of the classical phase space is investigated numerically via Poincare surfaces of section and corroborates the analytical results.
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