Scattering and local absorption for the Schroedinger operator

Technical Report · Sun Feb 01 04:00:00 EST 1976

OSTI ID:7323241

Combescure, M; Ginibre, J

For the Schroedinger operator H = - delta + V with potential V singular on a compact set epsilon of measure zero but sufficiently regular outside, the subspace of absolute continuity can be decomposed as the direct sum of a subspace of scattering states and a subspace of states locally absorbed on epsilon. This was proved by Pearson for dimension n = 3 and V belongs to L/sup 2/ + L to infinity away from epsilon. We extend this result to arbitrary dimension and to potentials that are only locally strictly delta-semibounded away from epsilon. In particular they may be strongly oscillating away from epsilon and have arbitrary behavior at infinity.

• Research Organization: Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique et Hautes Energies
• OSTI ID: 7323241
• Report Number(s): N-77-10927; LPTHE-76/4
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
HAMILTONIANS
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL OPERATORS
MATRICES
PERTURBATION THEORY
QUANTUM OPERATORS
S MATRIX
SCATTERING
SCHROEDINGER EQUATION
WAVE EQUATIONS