A semi-classical trace formula for Schrödinger operators in the case of a critical energy level

DOI10.1006/jfan.1996.3035zbMath0891.35130OpenAlexW2046392742MaRDI QIDQ1369771

David Khuat-Duy

Publication date: 19 July 1998

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

Full work available at URL: https://basepub.dauphine.fr/handle/123456789/6195

zbMATH Keywords

periodic orbitssemiclassical asymptoticsmicrolocal analysis

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) PDEs in connection with quantum mechanics (35Q40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items

Sharp semiclassical estimates for the number of eigenvalues below a totally degenerate critical level ⋮ Koszul complexes, Birkhoff normal form and the magnetic Dirac operator ⋮ Semiclassical asymptotic expansions for functions of the Bochner-Schrödinger operator ⋮ Spectral fluctuations of Schrödinger operators generated by critical points of the potential ⋮ A semi-classical trace formula at a non-degenerate critical level. ⋮ Semiclassical spectral estimates for Schrödinger operators at a critical energy level. Case of a degenerate minimum of the potential ⋮ Contributions of non-extremum critical points to the semi-classical trace formula ⋮ Semi-classical spectral estimates for Schrödinger operators at a critical level. Case of a degenerate maximum of the potential

Cites Work

• A semi-classical trace formula for Schrödinger operators
• L'asymptotique de Weyl pour les bouteilles magnétiques. (The Weyl asymptotic formula for magnetic bottles)
• Autour de l'approximation semi-classique. (Around semiclassical approximation)
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Circular symmetry and the trace formula
• Semiclassical principal symbols and Gutzwiller's trace formula
• The semi-classical trace formula and propagation of wave packets
• Spectral estimates around a critical level
• Fourier integral operators. I
• The uncertainty principle
• Oscillatory integrals, lagrange immersions and unfolding of singularities
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item