- 10-85 Sandro Graffi, Lorenzo Zanelli
- Geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schr dinger propagator
Jun 9, 10
(auto. generated pdf),
of related papers
Abstract. We construct a family of Fourier Integral Operators, defined for arbitrary large times, representing a global parametrix for the Schr dinger propagator when the potential is quadratic at infinity. This construction is based on the geometric approach to the corresponding Hamilton-Jacobi equation and thus sidesteps the problem of the caustics generated by the classical flow. Moreover, a detailed study of the real phase function allows us to recover a WKB semiclassical approximation which necessarily involves the multivaluedness of the graph of the Hamiltonian flow past the caustics.