Structure and Dynamics of Complex Excited Atomic Systems

In this project we plan to develop dimension-independent algorithms for solving the Schrödinger equation based on basis states related to a fictional single particle N-dimensional central field problem. The key ingredient will be to relate the formal ide ntity between the quantal many particle problem in D=N/n dimensions, where n is the number of particles and D is the physical dimension, to analytic features of the single particle quantal N-dimensional problem. Historically certain aspects of such scheme s were already explored, the new features of our project are the stress on generality and identification of structures suitable for massive numerical computations. The theoretical framework will be applied in the time-independent as well as time-dependen t domain: In the time-independent part a new classification scheme based on diagonalisation within the N-dimensional basis will be developed. In the time-dependent part a new split-step algorithm applicable for multiple number of particles will be develo ped and applied to many particle processes in strong fields.