Reciprocal Space and Crystals
For an electron (or other particle) in a crystal, its value of k relates almost always to its crystal momentum, not its normal momentum. Therefore k and p are not simply proportional but play different roles. See k·p perturbation theory for an example. Crystal momentum is like a wave envelope that describes how the wave varies from one unit cell to the next, but does not give any information about how the wave varies within each unit cell.
When k relates to crystal momentum instead of true momentum, the concept of k-space is still meaningful and extremely useful, but it differs in several ways from the non-crystal k-space discussed above. For example, in a crystal's k-space, there is an infinite set of points called the reciprocal lattice which are "equivalent" to k = 0 (this is analogous to aliasing). Likewise, the "first Brillouin zone" is a finite volume of k-space, such that every possible k is "equivalent" to exactly one point in this region.
For more details see reciprocal lattice.
Read more about this topic: Position And Momentum Space
Famous quotes containing the words reciprocal, space and/or crystals:
“I had no place in any coterie, or in any reciprocal self-advertising. I stood alone. I stood outside. I wanted only to learn. I wanted only to write better.”
—Ellen Glasgow (1873–1945)
“The woman’s world ... is shown as a series of limited spaces, with the woman struggling to get free of them. The struggle is what the film is about; what is struggled against is the limited space itself. Consequently, to make its point, the film has to deny itself and suggest it was the struggle that was wrong, not the space.”
—Jeanine Basinger (b. 1936)
“It is clear that everybody interested in science must be interested in world 3 objects. A physical scientist, to start with, may be interested mainly in world 1 objects—say crystals and X-rays. But very soon he must realize how much depends on our interpretation of the facts, that is, on our theories, and so on world 3 objects. Similarly, a historian of science, or a philosopher interested in science must be largely a student of world 3 objects.”
—Karl Popper (1902–1994)