1. Numerics on meshes vs. expansions on basis states in various physical problems L. Kocbach 1 University of Bergen, Norway

2. In solving the problems of quantum mechanics we most often solve Schr. equation There are naturally other problems, where a direct application of derived formalisms are appropriate, but this talk will not consider that. The task I talk about is thus: We wish to study a typical atomic physics problem

3. Schr. equation for N particles with possible external potentials/forces The equation can be time dependent The equation can be time independent Typical example: laser assisted collisions

4. ccc

5. After all the formulation is done and the model specified we can start solving it 1. setting up equation and finding solutions in terms of special functions 2. finding a well suited H_0, expand the solution in terms of eigenstates of H_0 3. Use a numerical solver of partial differential equations

6. ccc

8. Collisions inside subfemtoseconds laser pulsesPrague, November 4, 2002

9. Collision and laser pulse combined

10. Collisions inside subfemtoseconds laser pulsesPrague, November 4, 2002 Quantal formulation Schrödinger Equation Combination of projectile-electron and laser-electron interactions Dipole Approximation

11. Amplitude Equations – The traditional approach - Expansion