Realistic matrix elements of a Hamiltonian require careful evaluation, both the radial and angular integration can contain phases and constants which can easily lead to errors. Therefore, we will use very simple matrix elements instead. We only wish to study general behaviour of the time-dependent problems using codes (b) and (c).
Theory for tasks 2 and 3
See a picture of Correlation Diagram
In this task we are studying a simple time-dependent problem. It models the situation encountered in the atomic collision theory in the sense that it involves a position dependent hamiltonian.
In atomic collison theory, the eigenstates of the position dependent hamiltonian are called quasimolecular states, or (quasi) molecular orbitals (MO). It is customary to display them at so called correlation diagrams. One of the features of interest is the avoided crossing of the levels.
We assume that we study a (hypothetical) collision problem, which is sufficiently well described by 3 (or 4, 5 ...) states. Under Task 2, experiment with the provided input files and choose a model system that you wish to study in more detail.
The modifications involve changes of the 2 parameters for each of the matrix elements. Try some of the parameter combinations to model e.g. curve crossing. (see the explanation of the term curve crossing....)
The programs sjacob (task 2) and runge (task 3) use common input files. After choosing a suitable "collision system" in task 2, i.e. a certain combination of parameters, study velocity dependence of the collisional time development (task 3) Further, study the impact parameter dependence of this model scattering problem. This is the content of task 4
Instructions for task 2 .......... Instructions task 3
Description, All tasks
.......... Task 4.