The mathematical concept of Dirac notation

On 22.07.2014 and on 29.07.2014 I gave two lectures in our group seminar about the mathematical basis of Dirac notation.

Starting from the basic concepts of Euclidean spaces, the notes discuss Hilbert spaces and very briefly demonstrate that the set of square-integrable functions indeed forms a Hilbert space. Equipped with this knowledge we justify the use of Dirac notation using the so-called Riesz representation theorem.