Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our attention on the stability conditions permitting to control...

Arguments of the Jaynes' maximum entropy sort have proved to be surprisingly successful in providing one with approximate descriptions of pure states in a variety of scenarios, entirely bypassing any consideration of Schrödinger's equation. Thus far, however, the concomitant algorithm was...

The eigenvalue problem of an electron in the plane in the presence of a repulsive scatterer is studied. The electron is subject to a weak in-plane electric field and a magnetic field perpendicular to the plane. The associated magnetic length is much larger than the range of the scatterer. In...