Semiclassical Simple Initial Value Representations

Abstract

In this article, a class of Fourier Integral Operators which converge to the unitary group of the Schrödinger equation in semiclassical limit $\epsilon \to 0$ is constructed. The convergence is in the uniform operator norm and allows for a error bound $C_N{\epsilon }^{N+1}$ for any integer $N$ and extends to Ehrenfest timescaleswith bound $C_N{\epsilon }^{N+1-\rho }$ where $\rho$ can be made arbitrary small. In the chemical literature those approximations are known as simple Initial Value Representations.