Plans for week 41, October 6-10

Dear all, welcome back to FYS4480/9480.  This week we plan to

Thursday:

1. Stability of Hartree-Fock theory, wrapping up discussions from lecture October 3, see slides from last week

2. The homogeneous electron gas in three dimensions

       -Hartree-Fock solution and ground state energy

Friday:

1. Calculating the ground state energy of the electron gas

2. Discussion of first midterm

3. Lecture Material: These slides (see the attached pdf-file) and handwritten notes

4. First midterm set at https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/Exercises/2025/FirstMidterm2025.pdf. Available Friday October 10, deadline October 20, at midnight

The three-dimensional electron gas (3DEG) is a fundamental model in condensed matter physics that describes a system of non-interacting or weakly interacting electrons moving freely within a uniform positive background charge, ensuring overall charge neutrality. It provides a simple yet powerful framework for understanding the electronic properties of metals and doped semiconductors. In this model, electrons obey Fermi¨CDirac statistics, filling up quantum states in momentum space up to the Fermi energy.  At zero temperature, all states below the Fermi level are occupied, and excitations near the Fermi surface dominate the low-temperature thermodynamic and transport properties. Despite its simplicity, the 3DEG captures essential quantum many-body phenomena, such as screening, collective plasma oscillations, and the emergence of Fermi liquid behavior when interactions are included. It will also serve as a stepping stone towards our discussions of density functional theory since it provides this theory with the so-called local density approximation.

The first midterm will be available Friday the 10th and we will discuss elements of it during the lecture on Friday. The deadline is October 20. 

Yours,

Morten