Abstract
The very possibility of applying the modern methods of the classical theory of non-linear oscillations to quantum mechanics is based upon the representation of the non-stationary Schrödinger’s equation as a classical Hamiltonian system. From this perspective it is quite natural to construct a special asymptotic perturbation theory which utilises the advantages of the Hamiltonian formalism, that is to apply canonical transformations. Special and sufficiently efficient approaches [60], [35] and [29] were developed by mathematicians for canonical systems. However, the generality of these approaches makes them very cumbersome whereas the first two non-trivial approximations are ordinarily sufficient for practical application.
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© 2003 Springer-Verlag Berlin Heidelberg
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Nagaev, R.F. (2003). Canonical averaging of the equations of quantum mechanics. In: Dynamics of Synchronising Systems. Foundations of Engineering Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45761-9_6
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DOI: https://doi.org/10.1007/978-3-540-45761-9_6
Publisher Name: Springer, Berlin, Heidelberg
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