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Meaning of "reciprocal" in frequency space

by u0362565
Tags: frequency, meaning, reciprocal, space
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Jun16-14, 05:16 PM
P: 37
Hi all,

I'm curious about why reciprocal space is called precisely that. I always understood the reciprocal to be a word used in mathematics to describe the inverse or one divided by a number so how does that relate to frequency space unless in this case it means something completely different? Or is it perhaps linked to the mathematics of the Fourier transform?

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Jun16-14, 11:31 PM
P: 584
I guess it's called that because frequency is the reciprocal of a time period,

[itex]f = 1/T\;,[/itex]

and the corresponding things for wavelength, etc.
Jun17-14, 07:16 AM
P: 37
Ah yes that must be it. Thanks!

Jun17-14, 07:26 AM
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Meaning of "reciprocal" in frequency space

Please note that the term "reciprocal space" is more generic than that. In solid state/condensed matter, the reciprocal space is, literally, an inverse of real space. This is because things are described in units of wave number/vector, k, which is 1/length, and thus has a more appropriate designation of a "reciprocal space".

Jun17-14, 05:06 PM
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Reciprocal space is used to describe repeating patterns and has the axis in units of 'number per unit distance', as opposed to 'spacing'. I first came across it in Crystalography lectures where it can be used very conveniently to describe lattice structures and to work out the directions of diffracted beams of X rays. (The sums all fall out nicely when you do it that way.)

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