The file "ComalIterationSturmLiouville.pdf" contains a scan of an output of the comal programme "BACKFIT" and a scan of a print of the programme itself. 

The Danish text says "Kind regards Ole Trinhammer...Save the print for me..." as the output was written to a public printer. In line 0085 to 0086 of the programme is says " The machine is calculating, dear collegue...Ready by 'programme terminated' - please save the print for OT"

The outputs are parametric eigenvalues, i.e. eigenvalues for the 1-dimensional Schroedinger equation with approximate potential. The eigenvalues are used in the programme "MapleParametricFunctionGeneator.mw" to generate the parameter functions used in the programme "MathcadParametricBasis.mcd" to calculate eigenvalues for the exact 3-dimensional problem from the allospatial Hamiltonian.

The iteration is started off by a guess from the general trend in eigenvalues known from Sturm-Liouville theory and the theory of the harmonic oscillator. The individual integrations are started off with suitable boundary conditions according to the symmetry of the level sought. During the integration we keep track on the number of oscillations specific to the level sought for. If the number of oscillations is too large, the eigenvalue is adjusted downwards. Once the correct number of zeros has been reached the eigenvalue is fine-tuned by integrating backwards through the integration interval, i.e. from Pi back to 0, where we check that the boundary condition is correct. If not, the eigenvalue is adjusted accordingly.