Constructing quantum angular momentum l̂3 in a specific direction by using the U(1) group
The purpose of this work is to investigate the mathematical structure of finite quantum angular momentum in a specific direction L3 which can be constructed from the representation of the U(1) group. The angular momentum eigenstate is invariant under Abelian rotation symmetry. The character group of...
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| Format: | Article |
| Language: | English |
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Faculty of Science, Universiti Malaya
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/114376/ http://psasir.upm.edu.my/id/eprint/114376/1/114376.pdf |
| _version_ | 1848866475229577216 |
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| author | Rosli, Ahmad Aqwa Mohd Shah, Nurisya |
| author_facet | Rosli, Ahmad Aqwa Mohd Shah, Nurisya |
| author_sort | Rosli, Ahmad Aqwa |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The purpose of this work is to investigate the mathematical structure of finite quantum angular momentum in a specific direction L3 which can be constructed from the representation of the U(1) group. The angular momentum eigenstate is invariant under Abelian rotation symmetry. The character group of U(1) is constructed to show that there exists an additive unitary operator for the angular momentum eigenstate, and the rotation eigenstate is invariant under it. The Weyl relation is proved by showing that the angle eiϕ and angular momentum L3 are the canonical conjugate pair of observables © 2024 Faculty of Science, Universiti Malaya. All rights reserved. |
| first_indexed | 2025-11-15T14:21:11Z |
| format | Article |
| id | upm-114376 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:21:11Z |
| publishDate | 2024 |
| publisher | Faculty of Science, Universiti Malaya |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1143762025-01-20T00:50:28Z http://psasir.upm.edu.my/id/eprint/114376/ Constructing quantum angular momentum l̂3 in a specific direction by using the U(1) group Rosli, Ahmad Aqwa Mohd Shah, Nurisya The purpose of this work is to investigate the mathematical structure of finite quantum angular momentum in a specific direction L3 which can be constructed from the representation of the U(1) group. The angular momentum eigenstate is invariant under Abelian rotation symmetry. The character group of U(1) is constructed to show that there exists an additive unitary operator for the angular momentum eigenstate, and the rotation eigenstate is invariant under it. The Weyl relation is proved by showing that the angle eiϕ and angular momentum L3 are the canonical conjugate pair of observables © 2024 Faculty of Science, Universiti Malaya. All rights reserved. Faculty of Science, Universiti Malaya 2024-09 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/114376/1/114376.pdf Rosli, Ahmad Aqwa and Mohd Shah, Nurisya (2024) Constructing quantum angular momentum l̂3 in a specific direction by using the U(1) group. Malaysian Journal of Science, 43 (3). pp. 56-58. ISSN 1394-3065; eISSN: 2600-8688 https://mjs.um.edu.my/index.php/MJS/article/view/44397 Mathematical physics Quantum theory 10.22452/mjs.vol43no3.7 |
| spellingShingle | Mathematical physics Quantum theory Rosli, Ahmad Aqwa Mohd Shah, Nurisya Constructing quantum angular momentum l̂3 in a specific direction by using the U(1) group |
| title | Constructing quantum angular momentum l̂3 in a specific direction by using the U(1) group |
| title_full | Constructing quantum angular momentum l̂3 in a specific direction by using the U(1) group |
| title_fullStr | Constructing quantum angular momentum l̂3 in a specific direction by using the U(1) group |
| title_full_unstemmed | Constructing quantum angular momentum l̂3 in a specific direction by using the U(1) group |
| title_short | Constructing quantum angular momentum l̂3 in a specific direction by using the U(1) group |
| title_sort | constructing quantum angular momentum l̂3 in a specific direction by using the u(1) group |
| topic | Mathematical physics Quantum theory |
| url | http://psasir.upm.edu.my/id/eprint/114376/ http://psasir.upm.edu.my/id/eprint/114376/ http://psasir.upm.edu.my/id/eprint/114376/ http://psasir.upm.edu.my/id/eprint/114376/1/114376.pdf |