Canonical averaging of the equations of quantum mechanics

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.