Real Space vs Second Quantization

One day I thought to myself, let's learn about the nuclear shell model. Man, that was the beginning of quite the adventure. First off, where do you even start? I googled around for some time and found a few books and then some online resources. Along with this I felt mostly confusion. I think for most people nuclear physics is not really on the top of their list of things to learn. Probably having something to do with the difficulty of the subject. I'm not here to tell you the field is simple. I for sure am no expert, just a hobbyist. There are a few vocabulary things and concepts that I wish someone could have known before I started.

Hartree-Fock Approximation

Use a single slater determinant to represent your wavefunction with single-particle wavefunctions.

Full Configuration Interaction

This is a term that is used to describe the type of model used in nuclear physics. Interestingly it is also used in quantum chemistry because the problems are similar. In general, the method uses a set of slater determinants to create an eigenvalue problem with a single particle wavefunction. If you have to remember anything remember that the difference between hartree fock and FCI is that hartree fock uses one slater determinant and FCI uses many.

Real/Coordinate Space and Second Quantization

When you start solving FCI problems you have two distinct directions you can go. Real/Coordinate Space or Second Quantization. In Coordinate space you will explicitly write the slater determinants. In Second Quantization your representation will only allow the construction of antisymmetric wavefunctions. I started reading Heyde's book and it was nothing but coordinate space and wigner 3j, 6j, 9j symbols and then when I started looking around at more modern programs they use the second quantization formalism. There is good reason for this too, because it simplifies things a great deal. If for no other reason than understanding the value of second quantization you should make an effort to understand Coordinate space.

Excited and Ground State Determinants

So all those electron configuration problems you did in your into quantum chemistry course. They are now potentially useful. One can describe a determinant as excited or ground state.