Exact Relativistic to Non-Relativistic Transformation via an Effective Potential

Details Exact Relativistic to Non-Relativistic Transformation via an Effective Potential Exact Relativistic to Non-Relativistic Transformation via an Effective Potential

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aas...209.6807c&link_type=abstract

2007 AAS/AAPT Joint Meeting, American Astronomical Society Meeting 209, #68.07; Bulletin of the American Astronomical Society, V

Astronomy and Astrophysics

Astronomy

Scientific paper

We present a simple method for transforming a relativistic dynamical system into a non-relativistic dynamical system by introducing the “non-relativistic effective potential.” Thus, we are able to gain insight into the effects of relativity on particle dynamics by relying on our non-relativistic intuition. In particular, the particle velocity cannot exceed the speed of light because the effective force (negative gradient of the effective potential) approaches zero as the particle velocity approaches c. We demonstrate the procedure for several cases including the quadratic potential (Hooke’s Law spring) and a linear potential (string).

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