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?

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# Wave-Function, Fourier Transform, and Speed

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