Meaning of "reciprocal" in frequency space

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Discussion Overview

The discussion centers around the meaning of "reciprocal" in the context of frequency space and its relation to concepts in mathematics and physics, particularly in relation to the Fourier transform and solid state physics. Participants explore the terminology and its implications in various applications, including crystallography.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant questions the use of the term "reciprocal" in frequency space, linking it to its mathematical definition as an inverse or one divided by a number.
  • Another participant suggests that frequency is the reciprocal of time period, proposing that this relationship explains the terminology.
  • A later reply agrees with the previous point, indicating acceptance of the explanation.
  • One participant notes that "reciprocal space" is a more general term, emphasizing its use in solid state physics where it represents an inverse of real space, specifically in terms of wave number/vector.
  • Another participant mentions the application of reciprocal space in crystallography, highlighting its utility in describing lattice structures and predicting directions of diffracted X-ray beams.

Areas of Agreement / Disagreement

Participants express some agreement on the relationship between frequency and time period, but there are varying interpretations of the term "reciprocal" and its broader implications in different fields, indicating that multiple views remain in the discussion.

Contextual Notes

The discussion does not resolve the nuances of the term "reciprocal" as it applies across different contexts, and assumptions about its usage in various fields remain unaddressed.

u0362565
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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?

Thanks
 
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I guess it's called that because frequency is the reciprocal of a time period,

f = 1/T\;,

and the corresponding things for wavelength, etc.
 
Ah yes that must be it. Thanks!
 
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".

Zz.
 
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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