Weekly update September 20

Dear all, I hope this week started the best possible way for you all. Here comes the weekly digest.

Last week we started with eigenvalue problems and went through the basic philosophy of orthogonal transformations and discussed in more detail Jacobi's method (chapter 7.1-7.4 of the lecture notes). This method is not the most efficient one but offers several pedagogical benefits (easy to implement and offers a simple geometrical interpretation).   We started also to discuss project 2. We will continue our discussion of project 2 (in particular the two-electron case)  and link our results with the analytical ones presented by M Taut in https://journals.aps.org/pra/abstract/10.1103/PhysRevA.48.3561

This will allow us to benchmark our code against analytical solutions. Table 1 of that article contains a list of energies. It suffices to compare with one of these energies. Note that the author keeps the factor of 1/2 in the Schroedinger equation and that the eigenenergies are listed as functions of 1/ωr. For the first entry in that table the energy is 0.625. For the same frequency you should get twice the value. 

Else, this week we will discuss the famous Householder algo and how to obtain the eigenvalues of a tridiagonal matrix in a more efficient way. We will also discuss Lanczos' algorithm for finding eigenvalues of large matrices.  This material is discussed in the remaining sections of chapter 7.  It will also end ur discussion on eigenvalue problems. Next week we will start with ordinary differential equations and object orientation. 

At the lab we will use only some 30 mins of each session in order to demonstrate how to perform unit tests using catch. 

Next week at the Lab, Svenn-Arne Dragly (Phd student in Physics and now also a part-time employee of Qt) will give us a demonstration of advanced properties of Qt, from debugging and analysis of codes to more efficient usage of Qt. 

Best wishes to you all,

Morten