A Mathematical Justification for the Herman-Kluk Propagator

A class of Fourier Integral Operators which converge to the unitary group of the Schrodinger equation in the semiclassical limit epsilon -> 0 in the uniform operator norm is constructed. The convergence allows for an error bound of order O(epsilon), which can be improved to arbitrary order in epsilon 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.