Whats Fourier analysis?
“Fourier analysis” is a term that can be applied to the entire discipline which makes use of Fourier transforms: it’s a rich field with many powerful techniques for describing waves of any type. Here is the very basic idea behind Fourier analysis: you can actually make any function by superposing plane waves of different wavelengths (momenta in our case) and with different weights, in exactly the right way to get constructive and destructive interference to “sculpt” the shape of the function. It is actually pretty cool that this is possible for any function. The weights (in our particular case ) tell you “how much” of each momentum is present in the wave. This basic idea can be applied to lots of other situations (with real wave functions as well as complex ones). For instance, a sound wave can be a mixture of waves of different frequencies, and the Fourier transform of the wave tells you how much of each frequency is present. Try the links in the syllabus if you’re interested in
