The students know the definition of the Fourier-Transformation (FT) and learn about explicit examples. They know the properties and theorems of the FT, are able to apply these and describe physical processes both in time and frequency domain. They gain deep insights about physical processes analyzing the frequency domain and are able to utilize Fourier techniques solving physical problems, e.g. finding solutions of the time dependent Schrödinger equation. In addition, they learn about examples of the current english physical literature.
Content: Motivation: Applications of the FT in physics. Examples for Fourier paires, properties of the FT: symmetries, important theorems, shifting, differentiation, convolution theorem, uncertainty relation. Examples concerning the convolution theorem: frequency comb, Hilbert transformation, autocorrelation function. Methods of the time/frequency analysis and Wigner distribution. FT in higher dimensions: tomography. Discrete FT, sampling theorem. Applications in quantum mechanics