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The Adiabatic Invariance of the Action Variables

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Classical and Quantum Dynamics
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Abstract

We shall first use an example to explain the concept of adiabatic invariance. Let us consider a “super ball” of mass m, which bounces back and forth between two walls (distance l) with velocity v0. Let gravitation be neglected, and the collisions with the walls be elastic. If F m denotes the average force onto each wall, then we have

$$ {F_m}T = - \int_{coll.time} {f\;dt} \;. $$
(7.1)

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© 1992 Springer-Verlag Berlin Heidelberg

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Dittrich, W., Reuter, M. (1992). The Adiabatic Invariance of the Action Variables. In: Classical and Quantum Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97921-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-97921-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51992-8

  • Online ISBN: 978-3-642-97921-7

  • eBook Packages: Springer Book Archive

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