EXTENSIONS TO THE DISTRIBUTED APPROXIMATING FUNCTIONAL - THE HARMONICPROPAGATOR

The formalism of the distributed approximating functional for integrat ing the time-dependent Schrodinger equation is extended to allow an an alytic treatment of all Hamiltonians of quadratic order. The resulting propagator matrix is highly banded in both position and momentum repr esentations. For certain choices of the parameters, the action of this matrix can be cast in the form of a Toeplitz operator. We demonstrate that banded Toeplitz matrix-vector multiplication can be performed in significantly fewer numerical operations than is required by conventi onal split-operator fast Fourier transform algorithms. Numerical examp les verify the efficiency of this approach in both storage and speed. Extensions of the method to Monte Carlo path integration, and the impl ementation on massively parallel computer architectures, are discussed .