Hi, I'm pretty much an amateur in quantum mechanics. If anyone could clarify the following, that would be greatly appreciated!(adsbygoogle = window.adsbygoogle || []).push({});

When you write a wave-function (phi or "amplitude" for example) in terms of basis states (either position or momentum), does it undergo a Fourier decomposition? If so, do you actually perform it with respect to position, time, or both?

Does this process have anything to do with how momentum and position wave-functions are Fourier transforms of each other? Does this also have anything to do with the de Broglie relations (which one, frequency-energy or wavelength-momentum, or both as related through the constant c)?

Finally, regarding the basis states, are they also wave equations? If so, do their wave-numbers and frequencies have any relation to the wave-function undergoing decomposition, or can they be arbitrarily chosen? In either case, does the speed of a basis state wave-equation have any physical implications?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Wave-Function, Fourier Transform, and Speed

**Physics Forums | Science Articles, Homework Help, Discussion**