- #1
alphaone
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could somebody please explain to me why position and momentum space are related to one another by a fourier transform, meaning why do I get momenta when I do a fourier transform of an expression in position space?
could somebody please explain to me why position and momentum space are related to one another by a fourier transform, meaning why do I get momenta when I do a fourier transform of an expression in position space?
could somebody please explain to me why position and momentum space are related to one another by a fourier transform, meaning why do I get momenta when I do a fourier transform of an expression in position space?
Thanks for all your replies. I am sorry for having phrased my question badly. I know the mathematics of how to transform from position space to momentum space and how to get the fourier factor. However what I really shoud have asked is: Is there a physically intuitve reason why we would expect to get to momentum space when we do a fourier transform? By a physically intuitive reason I mean something along the same lines as calculating commutation relations of poincare generators with the Pauli-Lubanski vector: We could either plug in definitions and do the mathematics(which is a similar method to the earlier replies) or we could say that the pauli lubanski vector is a vector and so we know how it will transform under poincare transformations(which is kind of physically intuitive).
I am sorry, but I did not really understand your last reply. I am used to usual fourier analysis if that is what you mean, however I have never heard of a physical interpretation of such a transform and considering that it maps momentum space to position space and vice versa I was wondering whether such an interpretation exists. So if you know about any please let me know.
Are you asking why a wave packet can be described by some equationcould somebody please explain to me why position and momentum space are related to one another by a fourier transform, meaning why do I get momenta when I do a fourier transform of an expression in position space?
could somebody please explain to me why position and momentum space are related to one another by a fourier transform?
could somebody please explain to me why position and momentum space are related to one another by a fourier transform, meaning why do I get momenta when I do a fourier transform of an expression in position space?
Now, why is it that coordinate and wave number spaces related by the above Fourier transformation? well, the one and only answer is; because eq(F) represents the most general SUPERPOSITION of PLANE WAVES.
regards
sam