New approach to quantum dynamics: recursive, average case complexity, distributed approximating functional method for time-independent wavepacket forms of Schrِdinger and Lippmann-Schwinger equations

A new approach to quantum dynamics is presented which addresses the fundamental difficulty of exponential growth of computational complexity with the dimensionality of the system. A general recursive polynomial treatment of the time-independent full Green operator, the average-case complexity approach to multi-dimensional integration, and the continuous distributed approximating functional representation of the Hamiltonian are the three ingredients of the approach. Calculations for collinear H+H2 reactive scattering are presented to illustrate the method.