Hi - I have written a Fortran 'beginner' program to find the kinetic energy matrix for a simplistic non-relatavistic, 1-D, radial Schrodinger system - using the Lagrange - Laguerre Mesh method. Firstly, I have verified that my roots for the Laguerre poly ##L^{\alpha}_{N}(x_{i}) = 0## are correct for ##\alpha = 0##, they look OK for other values of ##\alpha##.(adsbygoogle = window.adsbygoogle || []).push({});

What I'd like to know, is if my kinetic elements ##T_{ij}## are at least in the right ballpark? I haven't been able to find any experimental or exact results to compare with. I have uploaded an output csv output file which I hope is self-explanatory - would appreciate any insights on the kinetic Matrix in the file please.

I am also looking for insight into why my matrix elements have alternating sign - I suspect a program bug :-(

I have sourced understanding & formulae from the rather impressive article - D Baye, Physics Reports 565, 1107 (2015) - and have appended the essential formulae section I used into the csv file.

Finally, the units are a little unclear to me, this is the first time I have done anything like this, I believe these eqtns are in natural units with ##\hbar## = 1, and m = 1 eV. I think the natural units are Gev, so my value are O(1Gev) which seems about right - but would really appreciate confirmation?

If you could comment on whatever aspects you can, all knowledge is useful, thanks.

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# Trying to verify my program's output

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