Task 2 and 3 . Description
## Task 2. and 3. Description

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 1
.......... Task 4.

Index