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Analytical Mechanics for Relativity and Quantum Mechanics$
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Oliver Johns

Print publication date: 2011

Print ISBN-13: 9780191001628

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780191001628.001.0001

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Angle‐Action Variables

Angle‐Action Variables

(p.509) 22 Angle‐Action Variables
Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Davis Johns

Oxford University Press

This chapter introduces the angle-action method and provides several examples of its use, including its essential role in the ‘old’ quantum theory, a precursor to the Schroedinger wave equation that sought to introduce quantum ideas into a classical model. Angle-action methods are also used in what is called canonical perturbation theory, the study of systems that deviate only slightly from cyclic ones. That vast subject is best studied using the language of differential geometry. Study of the present chapter will give the reader a firm grasp of the angle-action foundation upon which canonical perturbation theory is constructed. Certain specialised systems of importance in astronomy and quantum theory can be treated by a canonical transformation to angle-action variables.

Keywords:   angle-action method, old quantum theory, Schroedinger wave equation, canonical perturbation theory, differential geometry

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