By Niklaus Wirth
One of many vintage texts on facts constructions and algorithms! Examples are in Pascal.
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Extra info for Algorithms + Data Structures = Programs
After completion, we are able to compare the results with experimental data. The program described here closely follows the work of Toennies et al. who carried out various atomic collisions experimentally and modelled the results using a similar computer program . The program is built up in several steps. • First, the integration method for solving the radial Schrödinger equation is programmed. 1). • Second, we need routines yielding spherical Bessel functions in order to determine the phase shift via the matching procedure Eq.
8. Using these expressions, you can fill the overlap and the Hamilton matrix. Since both matrices are symmetric, it is clear that only the upper (or the lower) triangular part (including the diagonal) has to be calculated; the other elements follow from the symmetry. programming exercise Write a program in which the relevant matrices are filled and which solves the generalised eigenvalue problem for the variational calculation. 499 278 hartree, which is amazingly good if you realise that only four functions have been taken into account.
This will not be the case when two consecutive points are simply set to the solution Eq. 17), as this is not an exact solution to either the continuum differential equation or to its discrete (Numerov) form. You can adapt your program to the problem at hand by simply changing the function F(l, r, E) to contain the Lennard–Jones potential and by implementing the boundary conditions as described. As a check, you can verify that the solution does not become enormously large or remain very small. 2 The spherical Bessel functions For the present problem, you need only the first six spherical Bessel functions jl and nl , and you can type in the explicit expressions directly.
Algorithms + Data Structures = Programs by Niklaus Wirth