his thesis investigates the conserved Runge–Lenz vector in systems governed by inverse-square central forces. By analyzing its associated symmetries through the framework of Lie groups and Lie algebras, we explore its role in both classical and quantum mechanical settings. In eac
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his thesis investigates the conserved Runge–Lenz vector in systems governed by inverse-square central forces. By analyzing its associated symmetries through the framework of Lie groups and Lie algebras, we explore its role in both classical and quantum mechanical settings. In each case a hidden so(4) symmetry is revealed. In the classical regime, this is mapped to a SO(4) group action. Whilst in the quantum regime, this symmetry is used to calculate the energy levels of the hydrogen atom. This thesis was written as part of the Bachelor’s programs in Applied Physics and Applied Mathematics at Delft University of Technology
