Hidden Symmetries of the Kepler Problem in n Dimensions

Nobach, Destin (2023) Hidden Symmetries of the Kepler Problem in n Dimensions. Bachelor's Thesis, Mathematics.

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Abstract

This thesis focuses on the Kepler problem describing the motion of a particle under the influence of a central force according to an inverse-square law. A short review of the problem – as treated in standard (quantum) mechanics courses – is followed by an analysis of the underlying hidden symmetries. The main aim of this text is to study the n-dimensional generalisation of the Kepler problem, its solutions as well as the corresponding symmetry groups. This is realised by following to the ideas of Vladimir Fock where a Fourier transform on the Schrödinger equation associated to the quantum Kepler problem is considered, to then apply a stereographic projection. In this text an emphasis is put on the role quantum mechanical operators play in symmetry as a fundamental underpinning. In doing so, the framework of Lie groups and Lie algebras is introduced and employed.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Gorbe, T.F. and Veen, R.I. van der
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	31 Jul 2023 09:48
Last Modified:	31 Jul 2023 09:48
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/30995

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