Hamhuis, Jasper (2024) Harmonic Oscillators in Spaces of Constant Curvature. Bachelor's Thesis, Mathematics.
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Scriptie inzending van_ Jasper Hamhuis _ opleiding_ Mathematics.pdf Restricted to Registered users only Download (133kB) |
Abstract
In this thesis the N-dimensional simple harmonic oscillator is considered in three spaces of constant curvature, that is, in Euclidean, spherical and hyperbolic geometry. The orbits are derived in all three spaces: they are flat, spherical, and hyperbolic ellipses, respectively. For both classical and quantum mechanics, the tensor constants of motion are derived using Poisson bracket and commutator algebra, respectively. With these constants of motion, the Hamiltonian of the three dynamical systems are expressed as quadratic Casimir functions or operators of its symmetry group SU(N). Furthermore, the energy eigenvalues and eigenfunctions are derived by solving the Schrödinger equation in the three N-dimensional spaces.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Gorbe, T.F. and Seri, M. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 01 Jul 2024 07:52 |
| Last Modified: | 01 Jul 2024 07:52 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/32887 |
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