×

Semiclassical spreading of quantum wave packets and applications near unstable fixed points of the classical flow. (English) Zbl 0894.35026

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.

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
PDFBibTeX XMLCite