Essential spectrum of the main operators of quantum mechanics.
The aim of the talk is to present a new approach to the
investigation of the essential spectra of the main operators of
quantum mechanics. We include these operators in a class of
pseudodifferential operators perturbed by non-smooth potentials.
For an operator under consideration we introduce a family of limit
operators, and prove that the essential spectrum of the original
operator is the union of spectra of limit operators. Since the
limit operators have more simple structure than the original
operator, we obtain a strong tool for the investigation of the
essential spectra of differential and pseudodifferential operators.
We apply this method to the study of the essential spectra of the
Schrödinger, Klein-Gordon, and Dirac operators and to a new simple
proof of the classical Hunziker-van Winter-Zjislin Theorem.
