The regularized resolvent transform for quantum dynamics calculations

A recently introduced numerical expression for spectral estimation, called the regularized resolvent transform (RRT) (J. Magrl. Reson. 2000, 147, 129) , is shown to be very useful in a number of applications in quantum dynamic s calculations. RRT has emerged from the filter diagonalization method (FDM ), although it is based on a different linear algebraic algorithm and, ther efore, has different numerical properties, such as stability, robustness, s peed, etc. Given a time signal c(t), RRT provides a direct estimate of its infinite time Fourier spectrum Its). Replacement of the argument s in the R RT expression by -iE leads to a very useful formula to estimate the inverse Laplace transform of c(t). Two applications of RRT are discussed in detail : the calculation of all S-matrix elements using a single wave packet propa gation and the problem of estimating the microcanonical quantities, such as the density of states, from the canonical cross-correlation functions.