In this thesis, we determine an asymptotic solution for the one dimensional relativistic harmonic oscillator using multiple scale analysis and relate the resulting invariant to Lewis' invariant. We then generalize the equations leading to Lewis' invariant so they are relativistically correct. Next we attempt to find an asymptotic solution for the general equations by making simplifying assumptions on the parameter characterizing the adiabatic nature of the system. The first term in the series for Lewis' invariant corresponds to the adiabatic invariant for systems whose frequency varies slowly. For the relativistic case we find a new conserved quantity and seek to explore its interpretation.
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Master of Science (M.S.)
College of Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Reinhart, Daniel, "The Relativistic Harmonic Oscillator and the Generalization of Lewis' Invariant" (2019). Electronic Theses and Dissertations, 2004-2019. 6564.