Abstract
When the small angle approximation is not made, the exact solution of the simple pendulum is a Jacobian elliptic function with one real and one imaginary period. Far from being a physically meaningless mathematical curiosity, the second period represents the imaginary time the pendulum takes to swing upwards and tunnel through the potential barrier in the semi-classical WKB approximation1 in quantum mechanics. The tunneling here provides a simple illustration of similar phenomena in Yang-Mills theories describing weak and strong interactions.
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Cihan Saclioglu teaches physics at Sabanci University, Istanbul, Turkey. His research interests include solutions of Yang-Mills, Einstein and Seiberg-Witten equations and group theoretical aspects of string theory.
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Saclioglu, C. Swinging in imaginary time. Reson 15, 104–115 (2010). https://doi.org/10.1007/s12045-010-0012-x
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DOI: https://doi.org/10.1007/s12045-010-0012-x