Chen, Savio Ming Hou (2022) Generalisability of the LRL-vector: what the Kepler-Coulomb system can teach us about central potentials. Bachelor's Thesis, Physics.
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Abstract
Upon closer inspection of the Kepler-Coulomb problem a constant vector quantity is determined, revealing that the system admits a hidden symmetry. After investigating both the utility and interpretation of this invariant LRL-vector, other hidden symmetries are sought out. Through a mapping between the Kepler-Coulomb and two-dimensional harmonic oscillator, the latter is concluded to contain a conserved tensor. As only systems with specific potential energies could host a hidden symmetry, a modernised version of Bertrand's theorem is studied to learn about the qualified set of potentials. Classically, only the Kepler-Coulomb and harmonic oscillator potentials satisfy both the orbit equation and the closed orbit condition. Extension to include special relativistic effects provide a general solution of rather unusual form. Revealing that the classical solutions do not have closed orbits for all bound states in relativistic mechanics.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Roest, D. |
| Degree programme: | Physics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Jul 2022 14:09 |
| Last Modified: | 15 Jul 2022 14:09 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/27859 |
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