Diamond band structure

Tight Binding

Introduction There are many methods to calculate band structures of crystals. I implemented the Empirical Pseudopotential project, some of the code can be reused for other methods. One of the methods is simple and fast, the tight binding method, so I simply took the code from the last project, cut a part out and modified … Read moreTight Binding

d orbital

DFT for a Quantum Dot

Introduction This post is describing another project that is leading (hopefully) towards something a little more serious: DFT Quantum Dot1. It will be a very short description because it’s Sunday. As usual, here is the program in action: It displays the quantum dot ‘orbitals’ with VTK volume rendering. Do not assign much physical reality to … Read moreDFT for a Quantum Dot

Kohn-Sham equations

Density Functional Theory

Introduction As I already revealed in the last post, I intend to have several projects with Density Functional Theory on this blog. I already have a simple project on GitHub, about a ‘quantum dot’1 with volumetric visualization of orbitals with VTK. I thought that exposing some theory in a separate post would be nice for … Read moreDensity Functional Theory

CO2 molecule

The Hartree-Fock program

Introduction After some posts about the theory it is time to present the Hartree-Fock program1. You might find the previous posts useful, along with the links in there: How to solve a quantum many-body problem, The Hartree-Fock method. Here is the program in action (the final version might have minor differences): Although it doesn’t show … Read moreThe Hartree-Fock program

The Hartree-Fock method

Introduction Last time we ended up with a simplified Hamiltonian: and having the variational principle for help. It turns out that this simplified Hamiltonian is not simple enough. In this post I’ll expose one method that allows one to do calculations for quite complex quantum systems, the Hartree-Fock method. Because the subject is quite large, … Read moreThe Hartree-Fock method