Published February 1989
| Version v1
Journal article
Breit-Wigner formulas for the scattering phase and the total scattering cross-section in the semi-classical limit
Creators
- 1. Ecole Polytechnique, 91 - Palaiseau (France). Centre de Mathematique
- 2. Paris-11 Univ., 91 - Orsay (France). Dept. de Mathematiques
- 3. Nantes Univ., 44 (France). Dept. de Mathematiques
Description
In this paper we prove results in resonance scattering for the Schroedinger operator PV=-h2Δ+V, V being a smooth, short range potential on Rn. More precisely, for energy λ near a trapping energy level λ0 for the classical system defined by the Hamiltonian p(x, ζ)=ζ2+V(x), we prove that the scattering phase and the scattering cross sections associated to (PV, P0) have the Breit-Wigner form ('Lorentzian line shape') in the limit h → 0. (orig.)
Additional details
Publishing Information
- Journal Title
- Communications in Mathematical Physics
- Journal Volume
- 121
- Journal Issue
- 2
- Series
- Commun. Math. Phys.
- Journal Page Range
- 323-336
- ISSN
- 0010-3616
- CODEN
- CMPHA
INIS
- Country of Publication
- Germany
- Country of Input or Organization
- Germany
- INIS RN
- 20019793
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Descriptors DEI
- ASYMPTOTIC SOLUTIONS; BREIT-WIGNER FORMULA; EUCLIDEAN SPACE; HAMILTONIANS; INTEGRAL CROSS SECTIONS; INTERACTION RANGE; MANY-DIMENSIONAL CALCULATIONS; PHASE SHIFT; POTENTIAL SCATTERING; QUANTUM MECHANICS; RESONANCE; SCHROEDINGER EQUATION; SEMICLASSICAL APPROXIMATION
- Descriptors DEC
- CROSS SECTIONS; DIFFERENTIAL EQUATIONS; DISTANCE; ELASTIC SCATTERING; EQUATIONS; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM OPERATORS; RIEMANN SPACE; SCATTERING; SPACE; WAVE EQUATIONS