A Mathematical Justification for the Herman-Kluk Propagator

2007/12/05 by Swart, Torben, Rousse, Vidian · 1 citation
#35S30 #81Q20 #81S30 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0712.0752

Abstract

A class of Fourier Integral Operators which converge to the unitary group of the Schroedinger equation in semiclassical limit \eps→ 0 is constructed. The convergence is in the uniform operator norm and allows for an error bound of order O(\eps^1-ρ) for Ehrenfest timescales, where ρ can be made arbitrary small. For the shorter times of order O(1), the error can be improved to arbitrary order in \eps. In the chemical literature the approximation is known as the Herman-Kluk propagator.

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