Canonical perturbation

Since both initial and final states satisfy the same equations of motion, the transformation of Eq. (6) is a natural canonical transformation. This kind of canonical transformation is a basic tool in the so-called Lie canonical perturbation theory for obtaining approximate constants of the motion. 

A. Application of Canonical Perturbation Theory to Floppy Molecules... 

The purpose of this chapter is to review some properties of isomerizing (ABC BCA) and dissociating (ABC AB + C) prototype triatomic molecules, which are revealed by the analysis of their dynamics on precise ab initio potential energy surfaces (PESs). The systems investigated will be considered from all possible viewpoints—quanmm, classical, and semiclassical mechanics—and several techniques will be applied to extract information from the PES, such as Canonical Perturbation Theory, adiabatic separation of motions, and Periodic Orbit Theory. 

Here a and (3 are some constants depending on the system size N, as discussed in the following section. The proof of the theorem is reduced to evaluate the remainder terms after successive canonical perturbations, and it is possible to make the remainder exponentially small. 

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