CONSTRUCTING QUANTUM ANGULAR MOMENTUM L3 IN SPECIFIC DIRECTION BY USING U(1) GROUP

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Published: Sep 30, 2024
DOI: https://doi.org/10.22452/mjs.vol43no3.7
Keywords:
group character group group representation quantum angular momentum

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Ahmad Aqwa Rosli
Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 Serdang, Selangor, MALAYSIA.
https://orcid.org/0009-0007-0486-522X
Nurisya Mohd Shah
Department of Physics, Faculty of Scinec, Universiti Putra Malaysia, 43400 Serdang, Selangor, MALAYSIA.
https://orcid.org/0000-0001-7783-1118

Abstract

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 and angular momentum L3 are the canonical conjugate pair of observables.

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How to Cite
Rosli, A. A., & Mohd Shah, N. (2024). CONSTRUCTING QUANTUM ANGULAR MOMENTUM L3 IN SPECIFIC DIRECTION BY USING U(1) GROUP. Malaysian Journal of Science, 43(3), 56–58. https://doi.org/10.22452/mjs.vol43no3.7
Issue
Vol 43 No 3 (2024): September 2024
Section
Original Articles

Licensee MJS, Universiti Malaya, Malaysia. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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