### 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.
Time dependent Problem: Equations (1)

Explaining text

Equations solved by runge.f: Equations (2)

Index

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tdsep1.gif

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

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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)
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..............Equations (2)

**Real Correlation Diagram**

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expand.gif

Equations (1)
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..............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

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Index