The action variable and frequency of a relativistic harmonic oscillator
Theoretical and Mathematical Physics(2010)
摘要
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.
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关键词
Hamilton-Jacobi theory,action variable,relativity,simple harmonic oscillator
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