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
Links to introductory sections:
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. Read the Theory for the G-function Task .
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
Basic element in the semiclassical theory of collisions
THE RESULTS: explanations to task 4 (imprunge)
We calculate the probabilities for time functions corresponding to the trajectories.