Semiclassical asymptotics for the spectral function of long-range Schrödinger operators

DOI10.1016/0022-1236(89)90121-3zbMath0692.35069OpenAlexW1977399553MaRDI QIDQ583492

Christian Gérard, André Martinez

Publication date: 1989

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(89)90121-3

zbMATH Keywords

semiclassical asymptoticsspectral functioncomplex scalingBreit-Wignerespace functionlong range potentialsemiclassical Schrödinger operatorshape resonancestrapped trajectories

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items

Unnamed Item, Breit-Wigner formula for the scattering phase in the Stark effect, Resonance expansions of propagators in the presence of potential barriers., Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells. I, Mathematical study of scattering resonances, Limit measures for the Helmholtz equation in the non-trapping case, Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells II, Unnamed Item, Stationary scattering in the semi-classical limit for a Schrödinger operator in a gauge field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles
• Spectral asymptotics for elliptic second order differential operators
• The shape resonance
• Semiclassical resonances generated by a closed trajectory of hyperbolic type
• Semi-classical asymptotics for local spectral densities and time delay problems in scattering processes
• Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions
• A class of analytic perturbations for one-body Schrödinger Hamiltonians
• Multiple wells in the semi-classical limit I
• A complete asymptotic expansion of the spectral function for second-order elliptic operators inRⁿ
• A COMPLETE ASYMPTOTIC EXPANSION OF THE SPECTRAL FUNCTION OF SECOND ORDER ELLIPTIC OPERATORS IN $ \mathbf{R}^n$
• Résonances en limite semi-classique
• Estimations de l'effet tunnel pour le double puits. II : états hautement excités
• Oscillatory integrals, lagrange immersions and unfolding of singularities