The evolution of geometric Robertson–Schrodinger uncertainty principle for spin 1 system
Geometric Quantum Mechanics is a mathematical framework that shows how quantum theory may be expressed in terms of Hamiltonian phase-space dynamics. The states are points in complex projective Hilbert space, the observables are real valued functions on the space, and the Hamiltonian flow is specifie...
| Main Authors: | , , , |
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| Format: | Article |
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Lviv Polytechnic National University
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/103553/ |
| _version_ | 1848864047865266176 |
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| author | H., Umair H., Zainuddin K. T., Chan Sh. K., Said Husain |
| author_facet | H., Umair H., Zainuddin K. T., Chan Sh. K., Said Husain |
| author_sort | H., Umair |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Geometric Quantum Mechanics is a mathematical framework that shows how quantum theory may be expressed in terms of Hamiltonian phase-space dynamics. The states are points in complex projective Hilbert space, the observables are real valued functions on the space, and the Hamiltonian flow is specified by the Schr¨odinger equation in this framework. The quest to express the uncertainty principle in geometrical language has recently become the focus of significant research in geometric quantum mechanics. One has demonstrated that the Robertson–Schr¨odinger uncertainty principle, which is a stronger version of the uncertainty relation, can be defined in terms of symplectic form and Riemannian metric. On the basis of this formulation, we study the dynamical behavior of the uncertainty relation for the spin 1 system in this work. We show that under Hamiltonian
flow, the Robertson–Schr¨odinger uncertainty principles are not invariant. This is because, unlike the symplectic area, the Riemannian metric is not invariant under Hamiltonian flow
throughout the evolution process. |
| first_indexed | 2025-11-15T13:42:36Z |
| format | Article |
| id | upm-103553 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:42:36Z |
| publishDate | 2022 |
| publisher | Lviv Polytechnic National University |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1035532023-05-18T03:08:17Z http://psasir.upm.edu.my/id/eprint/103553/ The evolution of geometric Robertson–Schrodinger uncertainty principle for spin 1 system H., Umair H., Zainuddin K. T., Chan Sh. K., Said Husain Geometric Quantum Mechanics is a mathematical framework that shows how quantum theory may be expressed in terms of Hamiltonian phase-space dynamics. The states are points in complex projective Hilbert space, the observables are real valued functions on the space, and the Hamiltonian flow is specified by the Schr¨odinger equation in this framework. The quest to express the uncertainty principle in geometrical language has recently become the focus of significant research in geometric quantum mechanics. One has demonstrated that the Robertson–Schr¨odinger uncertainty principle, which is a stronger version of the uncertainty relation, can be defined in terms of symplectic form and Riemannian metric. On the basis of this formulation, we study the dynamical behavior of the uncertainty relation for the spin 1 system in this work. We show that under Hamiltonian flow, the Robertson–Schr¨odinger uncertainty principles are not invariant. This is because, unlike the symplectic area, the Riemannian metric is not invariant under Hamiltonian flow throughout the evolution process. Lviv Polytechnic National University 2022 Article PeerReviewed H., Umair and H., Zainuddin and K. T., Chan and Sh. K., Said Husain (2022) The evolution of geometric Robertson–Schrodinger uncertainty principle for spin 1 system. Mathematical Modeling and Computing, 9 (1). 36 - 49. ISSN 2312-9794; ESSN: 2415-3788 https://science.lpnu.ua/mmc 10.23939/mmc2022.01.036 |
| spellingShingle | H., Umair H., Zainuddin K. T., Chan Sh. K., Said Husain The evolution of geometric Robertson–Schrodinger uncertainty principle for spin 1 system |
| title | The evolution of geometric Robertson–Schrodinger uncertainty principle for spin 1 system |
| title_full | The evolution of geometric Robertson–Schrodinger uncertainty principle for spin 1 system |
| title_fullStr | The evolution of geometric Robertson–Schrodinger uncertainty principle for spin 1 system |
| title_full_unstemmed | The evolution of geometric Robertson–Schrodinger uncertainty principle for spin 1 system |
| title_short | The evolution of geometric Robertson–Schrodinger uncertainty principle for spin 1 system |
| title_sort | evolution of geometric robertson–schrodinger uncertainty principle for spin 1 system |
| url | http://psasir.upm.edu.my/id/eprint/103553/ http://psasir.upm.edu.my/id/eprint/103553/ http://psasir.upm.edu.my/id/eprint/103553/ |