Abstract
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.
Notes
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Graduation Date
2019
Semester
Summer
Advisor
Shivamoggi, Bhimsen
Degree
Master of Science (M.S.)
College
College of Sciences
Department
Physics
Degree Program
Physics
Format
application/pdf
Identifier
CFE0007712
URL
http://purl.fcla.edu/fcla/etd/CFE0007712
Language
English
Release Date
August 2020
Length of Campus-only Access
1 year
Access Status
Masters Thesis (Open Access)
STARS Citation
Reinhart, Daniel, "The Relativistic Harmonic Oscillator and the Generalization of Lewis' Invariant" (2019). Electronic Theses and Dissertations. 6564.
https://stars.library.ucf.edu/etd/6564