Plans for week 40, October 3-7

Hi all, we hope all is well!
Last week we discussed full configuration interaction theory and linked this with the usage of Wick's theorem and the calculation of explicit matrix elements (between many-body states with Slater determinants as basis states/computational basis). The wisdom is that if we can set up the so-called Hamiltonian matrix and diagonalize the problem, then this should provide us with all eigenpairs and in principle (although we may have truncated severely our Hilbert space) we should have solved the problem. If not, we need to deal with approximative methods. Our first method is Hartree-Fock theory, where we reduce the many-body problem to a set of coupled single-particle equations.  We will see also that this corresponds to a unitary transformation of the Hamiltonian matrix where we zero out the matrix elements that connect the 0p0h block with the 1p1h block.
The plan for this week is thus:
===== Week 40, October 3-7, 2022 =====
* Topics to be covered
  o Thursday:
    * Repetition  of Full Configuration Interaction theory
    * Start Hartree-Fock theory
    * "Video of lecture":"https://youtu.be/"
  o Friday: 
    * Hartree-Fock theory and stability of equations
    * "Video of lecture":"https://youtu.be/"
* Lecture Material: These slides, handwritten notes and Szabo and Ostlund, sections 3.1-3.4
* Sixth exercise set at https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/Exercises/2022/ExercisesWeek40.pdf

This exercise is a continuation of our discussion of the Lipkin model, but now with a full FCI calculation, but also for week 41, a Hartree-Fock calculation.

Best wishes to you all,
Morten and ?yvind