Annales Henri Poincaré

, Volume 3, Issue 6, pp 1215–1232

Propagation Properties for Schrödinger Operators Affiliated with Certain C*-Algebras

  • W. O. Amrein
  • M. Mantoiu
  • R. Purice
Original article

DOI: 10.1007/s000230200003

Cite this article as:
Amrein, W., Mantoiu, M. & Purice, R. Ann. Henri Poincaré (2002) 3: 1215. doi:10.1007/s000230200003

Abstract.

We consider anisotropic Schrödinger operators \( H = -{\Delta} + V \) in \( L^{2}(\mathbb{R}^n) \). To certain asymptotic regions F we assign asymptotic Hamiltonians HF such that (a) \( \sigma(H_F) \subset \sigma_{\textrm{ess}}(H) \), (b) states with energies not belonging to \( \sigma(H_F) \) do not propagate into a neighbourhood of F under the evolution group defined by H. The proof relies on C*-algebra techniques. We can treat in particular potentials that tend asymptotically to different periodic functions in different cones, potentials with oscillation that decays at infinity, as well as some examples considered before by Davies and Simon in [4].

Copyright information

© Birkhäuser Verlag Basel, 2002

Authors and Affiliations

  • W. O. Amrein
    • 1
  • M. Mantoiu
    • 2
  • R. Purice
    • 2
  1. 1.Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland, e-mail: Werner.Amrein@physics.unige.chCH
  2. 2.Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest, RO-70700, Romania, e-mail: Marius.Mantoiu@imar.ro and e-mail: Radu.Purice@imar.roRO