Two forms of the action variable for the relativistic harmonic oscillator

2007/02/11 by M. K. Balasubramanya, Balasubramanya, M. K.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0702036

arxiv created 2007/02/11 · arxiv updated 2009/12/01

Abstract

The frequency of a classical periodic system can be obtained using action variables without solving the dynamical equations. We demonstrate the construction of two equivalent forms of the action variable for a one dimensional relativistic harmonic oscillator and obtain its energy dependent frequency. This analysis of oscillation is compared with the traditional solution of the problem which requires the use of hypergeometric series.

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