The non-supersymmetric (F=0) case reproduces old results by M. Lüscher and G. Münster (Nucl. Phys. B232 (1984) 445), and those I obtained in collaboration with Jeff Koller. See also another paper with him, which forms essential background for this study. The very first time I discussed in writing (with little success) the problem of the adiabatic approximation for determining the Witten Index was in September 1991. Writing a recent review on QCD in a finite volume, prompted me to come back to this problem. The background material for the supersymmetric analysis can be found in the paper "The Witten index beyond the adiabatic approximation" [hep-th/0112072], which is dedicated to the memory of Michael Marinov.

Here is the Mathematica code for generating the basis and matrix elements.
I did **not** use Mathematica Notebook features, so that the available
code should run on any platform. It has been tested with Mathematica
versions 2.0, 3.0 and 4.0. *Use each mathematica program in a separate
session, such that global definitions do not interfere*!

- Generate.ma, creates spherical harmonics and makes tables of reduced matrix elements (Htab0r, HHtab0r, Htab2r, and HHtab2r) in a format suitable for input in Fortran programs.
- Besj.ma, computes radial matrix elements and makes tables (Rtab2 and RRtab2) suitable for input in Fortran programs.
- Bjtab.ma, makes table (Bjtab) of spherical Bessel functions in a format suitable for input in Fortran programs and used to reconstruct the wave function.
- roots.out, roots of the derivative of the spherical Bessel functions needed in Besj.ma, to make radial matrix elements.

- H0t.ma, builds the full matrix for the F=0 (bosonic) case, allows for diagonalization with mathematica and building the wave function (slow but manageable). Also makes a table for the full matrix (Htab0) in a format suitable for input in Fortran programs.
- H2t.ma, builds the full matrix for the F=2 case, allows for diagonalization and Temple's inequality with mathematica (not advised, except for testing). Also makes tables for the full matrix (Htab2 and HHtab2) in a format suitable for input in Fortran (also not advised, except for testing).

- H2h.ma, builds the full matrix for the F=2 case with harmonic oscillator basis, allows for diagonalization and makes a table (Htab2h) for the full matrix in a format similar to Htab0 and suitable for input in Fortran.

- diag.f, used for diagonalizing H(r), computing Veff, diagonalizing H and reconstructing the groundstate wave function. It allows for automatic pruning. Read the extensive comments. See also here.

Page initially created on 10 December 2001. Any changes in the programs can be detected from their version date listed in the beginning.

**Disclaimer**: Users themselves are responsible for the results obtained
with these programs.

This is free code. Of course it has been tested
extensively, but I can give no guarantees.

Pierre van Baal, last updated 14 September 2004.