Gheorghe Nenciu
On asymptotic perturbation theory for Quantum Mechanics: Almost
invariant subspaces and gauge invariant magnetic perturbation theory
(320K, Postscript)
ABSTRACT. Singular perturbation theory for Quantum Mechanics is considered in a framework
generalising the spectral concentration theory.
Under very general conditions, asymptotic estimations on the
Rayleigh-Schroedinger expansions of the perturbed spectral projections are
obtained. As a consequence almost invariant subspaces of exponential order
are constructed. The results cover practically all singular perturbations
considered in nonrelativistic quantum mechanics. In the magnetic field case,
under the condition that the magnetic field does not increase at infinity,
a gauge invariant perturbation theory leading to convergent series with
field dependent coefficients is developed.