JournalsrlmVol. 22, No. 1pp. 17–28

Global parametrices for the Schrödinger propagator and geometric approach to the Hamilton-Jacobi equation

  • Sandro Graffi

    Università di Bologna, Italy
  • Lorenzo Zanelli

    Università di Bologna, Italy
Global parametrices for the Schrödinger propagator and geometric approach to the Hamilton-Jacobi equation cover
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Abstract

A result is announced concerning a family of semiclassical Fourier Integral Operators representing a global parametrix for the Schrödinger propagator when the potential is quadratic at infinity. The construction is based on the geometrical approach of 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.

Cite this article

Sandro Graffi, Lorenzo Zanelli, Global parametrices for the Schrödinger propagator and geometric approach to the Hamilton-Jacobi equation. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), no. 1, pp. 17–28

DOI 10.4171/RLM/585