Combescure, M.; Robert, D. Semiclassical spreading of quantum wave packets and applications near unstable fixed points of the classical flow. (English) Zbl 0894.35026 Asymptotic Anal. 14, No. 4, 377-404 (1997). The authors investigate the spreading of coherent states under the time evolution generated by the Schrödinger operator. This extends previous work of P. Hagedorn [Ann. Phys. 135, 58-70 (1981) and Ann. Inst. H. Poincaré, Phys. Theor. 42, 363-374 (1985)] and others. The main result is a precise asymptotic expansion of the time dependent solution of the Schrödinger equation for these initial states. They use their result to show that the spreading is exponential on a time scale given by the usual Ehrenfest time provided the state is centered around an unstable fixed point of the classical flow. Reviewer: Heinz Siedentop (Regensburg) Cited in 1 ReviewCited in 32 Documents MSC: 35J10 Schrödinger operator, Schrödinger equation 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 35C20 Asymptotic expansions of solutions to PDEs Keywords:spreading of coherent states; precise asymptotic expansion PDFBibTeX XMLCite \textit{M. Combescure} and \textit{D. Robert}, Asymptotic Anal. 14, No. 4, 377--404 (1997; Zbl 0894.35026)