TalentDFT

• Install Git, and try out some of the commands covered in Morten or Nicolas's lecture slides (computing.pdf talentdftguides.pdf) for your codes in the following problems.

• In your favorite programming language, make a program to construct a real symmetric $NxN$ matrix. Diagonalize it using the appropriate LAPACK or GSL routine, and write out some number of the lowest eigenvalues. (Suggestion: You might find it useful to use Mathematica (available on the ECT* computers) to diagonalize a small matrix that you can benchmark against.) This will help you test that you've linked to the GSL or LAPACK library.

• The code coulomboscrelme.f90.zip calculates the relative matrix elements $\langle nl|V|n'l\rangle$ in HO states. From this, construct a subroutine that returns the properly normalized $r$-space HO wf's. For some basic background on HO wf's, see here.

• Check numerically that the constructed HO wf's are orthonormal. To do this, you will want to use Gaussian quadrature to discretize the integrals. Gaussian quadrature is discussed a bit in . If you don't have a routine to calculate quadrature points/weights, take advantage of Google to find a canned routine to do this for you.

• Construct the matrix $\langle nl|T+V|n'l\rangle$

• Construct a subroutine that returns relative HO matrix elements of the Minnesota NN potential. The definition of the Minnesota potential and a sketch of how to proceed will be given on the black board.

Here are