GEOMETRIC APPROACH TO THE HAMILTON–JACOBI EQUATION AND GLOBAL PARAMETRICES FOR THE SCHRÖDINGER PROPAGATOR

DOI10.1142/S0129055X11004497zbMath1308.47053MaRDI QIDQ2889719

Sandro Graffi, Lorenzo Zanelli

Publication date: 8 June 2012

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

symplectic geometrySchrödinger equationglobal Fourier integral operatorsmultivalued WKB semiclassical method

Mathematics Subject Classification ID

Lagrangian submanifolds; Maslov index (53D12) Fourier integral operators applied to PDEs (35S30) Schrödinger and Feynman-Kac semigroups (47D08)

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Cites Work

• Unnamed Item
• Smoothness and non-smoothness of the fundamental solution of time dependent Schrödinger equations
• Symplectic topology as the geometry of generating functions
• A mathematical justification for the Herman-Kluk propagator
• Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent
• On a nature of convergence of some Feynman path integrals. II
• Fourier integral operators. I
• Spectre D'Un hamiltonien quantique et mecanique classique
• ON THE BEHAVIOR AT INFINITY OF THE FUNDAMENTAL SOLUTION OF TIME DEPENDENT SCHRÖDINGER EQUATION
• The global finite structure of generic envelope loci for Hamilton–Jacobi equations
• Periodic solutions of asymptotically linear Hamiltonian systems
• On the fundamental solution of semiclassical Schrödinger equations at resonant times