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This article is cited in 1 scientific paper (total in 1 paper)
The action variable and frequency of a relativistic harmonic oscillator
M. K. Balasubramanya Department of Physical and
Environmental Sciences, Texas A&M
University-Corpus Christi, Corpus Christi, USA
Abstract:
We present three series representations of the frequency of a relativistic harmonic oscillator. The first two representations use two equivalent forms of the action variable. The third representation involves determining its period by direct integration. The energy dependance of the oscillator frequency is manifestly seen in all three representations. We demonstrate that all three forms yield the same expression for the frequency in the case of the weakly relativistic oscillator and have an identical nonrelativistic limit.
Keywords:
Hamilton–Jacobi theory, action variable, relativity, simple harmonic oscillator.
Received: 24.03.2009
Citation:
M. K. Balasubramanya, “The action variable and frequency of a relativistic harmonic oscillator”, TMF, 162:3 (2010), 408–415; Theoret. and Math. Phys., 162:3 (2010), 341–346
Linking options:
https://www.mathnet.ru/eng/tmf6478https://doi.org/10.4213/tmf6478 https://www.mathnet.ru/eng/tmf/v162/i3/p408
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