1. The problem statement, all variables and given/known data The position and momentum wavefunctions are fourier transform pairs. If a particle has a perfectly defined position wavefunction Psi(x) = delta(x - x0), then what is its momentum wavefunction? Is this function normalizable? 2. Relevant equations Fourier transform relation (Can't figure out how to use the latex inputs to write this out) 3. The attempt at a solution I think I have to take the fourier transform of a dirac delta "function"... I believe this is just a single frequency sine or cosine wave, but I only think this based on intuition from what the fourier transform means. As far as if this function is normalizable, I'm not really sure what is meant by that. Does that mean you take the integral over all space (or in this case all momentums) of the wavefuntion squared and set it equal to 1? Any help/advice on this would be much appreciated. Its been a while since I've studied quantum. Thank you.