Abstract
Let \(q_{1},q_{2},\ldots,q_{N},p_{1}.p_{2},\ldots p_{N}\) be 2N independent canonical variables, which satisfy Hamilton’s equations:
We now transform to a new set of 2N coordinates Q 1, … Q N , P 1, … P N , which can be expressed as functions of the old coordinates:
These transformations should be invertible. The new coordinates Q i , P i are then exactly canonical if a new Hamiltonian K(Q, P, t) exists with
Our goal in using the transformations (6.2) is to solve a given physical problem in the new coordinates more easily.
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Dittrich, W., Reuter, M. (2016). Canonical Transformations. In: Classical and Quantum Dynamics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-21677-5_6
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DOI: https://doi.org/10.1007/978-3-319-21677-5_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21676-8
Online ISBN: 978-3-319-21677-5
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