Theory for Task 2 and 3

This is a page describing the basis of the (semi) classical collision theory, as suitable for Task 2 and Task 3.

Equations solved by runge.f: Equations (2)

Equations (2) .............. TOP ..............Explaining text

The theory: Time dependent Schroedinger equation relevant for the collision process. The expansion in a basis set is shown. Also shown are the kinetic energy of the electron and the two potentials, describing the interaction with the target and the projectile.

The static case for an instantaneous hamiltonian corresponds to finding the eigenstates of H(R) for given t .

Task 2

In our model case, sjacob.f (Task 2) is diagonalizing the model H(R) . We obtain a model correlation diagram, i.e. the eigenvalues as function of R .

Equations (1) ..............TOP ..............Equations (2)

Real Correlation Diagram

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Equations (1) ..............TOP ..............Explaining text

Task 3

Using the expansion and evaluating projections on the basis states, one obtains a set of coupled equations for the coefficients as functions of time.
By obtaining the expansion coefficients, we can calculate the occupation probabilities (and the experimentally relevant quantities) (The expansion coefficients are sometimes called "c", sometimes "a" !!)

Definition of Probability and Cross Section cross.html

Index