Weekly plans and update for week 38

Dear All, here comes our weekly summary from last week and plans for this Thursday and Friday, lectures and labs.

At the lab we continue working on project 2.

Last week, we started discussing the mathematics of project 2 and looked at how we could convert a one-dimensional 2nd-order differential equation with two boundary constraints (a so-called two-point boundary value problem) into an eigenvalue problem. The matrix to diagonalize is the same as the one we discussed in project and you are tasked with writing a code which implements the Jacobi rotation algorithm.

This week, Thursday, we keep discussing this algorithm and extend our cases to study to a quantum-mechanical one (for those not familiar with this, just view it as a numerical problem similar to the starting case (parts a and b).

We discuss again how to scale the equations and discuss in more detail project 2.

A new element is the introduction of unit tests and we will discuss how to implement these in c++, example codes are at https://github.com/CompPhysics/ComputationalPhysics/tree/master/doc/Projects/2020/Project2/CodeExamples  We will discuss these codes and one unit test library in C++ that has become very popular, catch++ https://github.com/catchorg/Catch2/blob/master/docs/tutorial.md

We will also start discussing other methods for obtaining eigenvalues  via steps such as Householder transformations, Lanczos' iterative scheme, the power method and the QR method. Householder's method and these other ones are discussed in chapters 7.4-7.7  of the lecture notes, as well as in the eigenvalue slides, see http://compphysics.github.io/ComputationalPhysics/doc/pub/eigvalues/html/._eigvalues-bs000.html

These topics are discussed on Friday as well, meaning that we will most likely end our eigenvalue discussion at the beginning of next week. 

Best wishes to you all,

Aksel, Anders, Kaspara, Maria, Morten, Rene og Sebastian