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Noncovariant Lagrangians Are Presented Which Yield Two-Component Equations of Motion for a Class of Relativistic Mechanical Systems in 1 + 1 Dimensions Including the Harmonic Oscillator
Department of Physics and Astronomy, University of Georgia, Athens, Georgia, USA
- 1 Department of Physics and Astronomy, University of Georgia, Athens, Georgia, USA
Applied Mathematics·Volume 11 (2020)·Pages 917–921·Published 1 September 2020·DOI10.4236/am.2020.119059
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Abstract
First, a Lagrangian is presented and authenticated for a Relativistic Harmonic Oscillator in 1 + 1 dimensions. It yields a two-component set of equations of motion. The time-component is the missing piece in all previous discussions of this system! The second result is that this Oscillator Langrangian generalizes to Langrangians for a class of particles in 1 + 1 dimensions subject to an arbitrary potential V which is space dependent only.
KeywordsHarmonic Oscillator
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