List of Topics:Their Purpose

### List of Topics: Their Purpose

Each of the links brings you to description of the topic's purpose. Below in this page, we give a combined and unified version of these individual explanations

### Individual descriptions of the purpose

```
Introduction     general introduction, physics
About Experiment concept of cross section, coincidence...
G-functions      Details of one aspect
TDSE-Static      Atomic x Molecular
TDSE-Time        Time dependent quantum mechanics
TDSE-Impact Parameter  From Q.M. to experiment
Picture Analysis-Movie Scientific Visualization
Report                 Something to remember

Index

Unified description of the course ( purpose )

Introduction

Here we need to introduce the computers, repeat the theory
from the general text and define the
structure.

How to work
The Theory of Atomic Collisions
Definition of Cross Section cross.html
The Theoretical basis of task 1

Experiment etc
This is a reading section, shows relation to other fields

concept of cross section, coincidence...

G-functions
The single-centre problem is described in file (gfun.tex)
which should be included in the general description.

This task has been included because
it is possible to see all the complexity of the problem,
and still the simple concept of the radial G-functions.

Relation of Static and instantaneous basis sets
In this section we work with a model hamiltonian.

THE RESULTS: explanations to task 2 and 3

The form is
H =  H0 + V(t)
and in the fixed basis it is given by a matrix
The R-dependence of the matrices is of a single form

The purpose is to show (especially in the next task)
the relation between
static basis set time-dependent theory
and
time-dependent theory based on instantaneous eigenstates
i.e.
basis set of so-called adiabatic perturbation theory.

Here we practice some "Matrix Mechanics", by finding the
eigenvalues and looking at the R-dependence of the
eigenstates

Here we use the Runge-Kutta method to solve the
equations for  coefficients in expansion of Wave Function
in TDSE.

THE RESULTS: explanations to task 2 and 3

Basic element in the semiclassical theory of collisions

Impact Parameter introduced

This shows again a "more practical" relation to the
experimental situation.

THE RESULTS: explanations to task 4 (imprunge)

We calculate the probabilities for time functions
corresponding to the trajectories.

And here are again links to the individual descriptions of the purposes

Introduction     general introduction, physics
About Experiment concept of cross section, coincidence...
G-functions      Details of one aspect
TDSE-Static      Atomic x Molecular
TDSE-Time        Time dependent quantum mechanics
TDSE-Impact Parameter  From Q.M. to experiment
Picture Analysis-Movie Scientific Visualization
Report                 Something to remember

Index

```