*If you follow this course in sync with the live classes (September-December), then this chapter is your main content for week 7 of the fall term (see list of due dates). *

DFT has been developed by theoretical condensed matter physicists, before it became sufficiently mature to enter the area of materials science. As a consequence, some of the natural ingredients of DFT codes originate from the field of electronic structure theory. You’ll inevitably get into contact with these concepts if you read about DFT calculations, even if you focus on applied papers. Therefore, it is very useful to have a basic understanding of those.

If you are a physicist, then the topics of this chapter will feel familiar (although I bet they are presented in a way that you may find surprising). If you are a chemist or a material scientist, then you will get closer to condensed matter theory then ever before (but no worries, we try hard to present it in a way that makes sense to you).

Going thoroughly through this chapter, will take you about 1h40m.

In the separate hands-on section **(test yourself)** you learn how to calculate a band structure and a density of states picture for a crystal. This task is integrated in the tasks of this week, and will not require additional work this week.

**If you participate in the project, don’t forget to submit this week your second milestone.**

Space as we know it — the 3-dimensional environment in which we live and in which crystals exist, an environment called *direct space* in this context — can be represented in a different way as ‘reciprocal space’. Kohn-Sham solvers make use of it a lot.

**Expected time: 10m**

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Within the reciprocal space lies the reciprocal lattice, which reflects useful aspects of the crystal symmetry. You will learn how to transform between the Bravais lattice of a crystal in direct space, and its reciprocal lattice in reciprocal space.

**Expected time: 15m**

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The state of a quantum system is labeled by so-called ‘quantum numbers’. We revisit this concept

**Expected time: 10m**

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One can learn a lot about a quantum system by inspecting a plot of its single-particle orbitals.

**Expected time: 20m**

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If a crystal is a quantum system, what are its quantum numbers? You will see there are many, really many quantum numbers needed. Hence, we will discuss various ways to condense this information into a manageable form.

**Expected time: 40m**

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Are you still on board?

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Here you can find the recording of the feedback webinar of this week.

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