Understanding the Fourier Transform and Its Applications

[occhi]

The Fourier transform relates spacetime domain to momentum-energy (wave number - frequency) domain. For example, a generic function f(x, t) is transformed as given by photo

I can't understant What does this theorem guarantee about the quantum systems?Hot to find the representation of momentum in position space.?

thank you!

 

[Matterwave]

The Fourier transform transforms your position representation wave-function into a momentum (or wave-number)-representation wave-function. In Dirac notation, it would take <x|psi> and transform it into <p|psi>. Where |psi> is just some state vector that includes all of the information you could obtain about a particle.