A Mathematical Justification for the Herman-Kluk Propagator

A class of Fourier Integral Operators which converge to the unitary group of the Schrödinger equation in the semiclassical limit ε → 0 in the uniform operator norm is constructed. The convergence allows for an error bound of order O(ε), which can be improved to arbitrary order in ε upon the introduction of corrections in the symbol. On the Ehrenfest-timescale, the result holds with a slightly weaker error bound. In the chemical literature the approximation is known as the Herman-Kluk propagator.