# Perturbation theory and control in classical or quantum mechanics by an inversion formula

@article{Vittot2003PerturbationTA, title={Perturbation theory and control in classical or quantum mechanics by an inversion formula}, author={M. Vittot}, journal={Journal of Physics A}, year={2003}, volume={37}, pages={6337-6357} }

We consider a perturbation of an 'integrable' Hamiltonian and give an expression for the canonical or unitary transformation which 'simplifies' this perturbed system. The problem is to invert a functional defined on the Lie-algebra of observables. We give a bound for the perturbation in order to solve this inversion, and apply this result to a particular case of the control theory, as a first example, and to the 'quantum adiabatic transformation', as another example.

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