Talk:Wave vector

Introductory section

Comments

• A wave vector is not a vector representation of a wave unless one introduces a function space, a set of orthonormal basis functions, and a way to describe any arbitrary wave as a vector in the function space using the basis functions. The author has clearly not explained any of the details to the reader. Furthermore, any such discussion does not belong in the introductory paragraph of the wave vector article.
• The author states that a single wave vector describes a family waves. What does the author mean? I offer the following different scenarios and comments. (a) The author means that any arbitrary wave is really a family of basis functions with the wave vector giving the appropriate coefficients. In this case, the meaning is totally lost. (b) The author means that a single point disturbance in time constitutes a wave and that a spatially extended collection of point disturbances in time constitutes a family of (presumably temporal) waves. This idea culminates with the confusing statement that a family of waves is exemplified by a plane wave in one spatial dimension. The author unsuccesfully tries to make a distinction between waves in time and space. Introducing such a distinction to explain the concept of a wave vector is unnecessary. Furthermore the distinction between temporal and spatial oscillations is already made in the waves article. Therefore the first section of the wave vector article should focus on the spatial characteristic of the wave. Then the more advanced section on four vectors etc. can discuss both the spatial and temporal characteristics of the wave. (c) The author confuses the ideas in points a and b. (d) I think I finally understand. The author means that a plane wave is a family of one dimensional waves. In other words one could imagine constructing an infinite plane by stacking an infinite number of lines. To get a plane wave the lines just need to have sinusoidal oscillations of the same wavenumber, frequency, and initial phase. Here a picture would be worth a thousand words. The meaning is totally lost.
• In any event a single wave vector describes a single plane wave.
• The introductory section needs a major rewrite.

Edits

• Remove the following statements.

The wave vector is a vector representation of a wave.

The wave vector is most useful for generalizing the equation of a single wave into a description of a family of waves. As long as the family of waves all travel in the same direction and with the same wavelength, a single wave vector is valid for the entire family. The most common case of a family of waves that meets these requirements is the plane wave, in which the family of waves is also coherent, i.e. all the waves have the same phase.

• Replace

That last step where it equals zero, is a result of the fact that, for light, k=ω/c

with

That last step where it equals zero, is a result of the fact that, for light, k⁰=k₀=ω/c

Hi, I am just wondering if its 'wavevector' or 'wave vector' or even 'wave-vector'? A google search didn't help me to draw a conclusion... Thanks, Splette :) ^{How's my driving?} 20:16, 15 January 2008 (UTC)

I sorted out the disambiguation and re-directed it here. LOTRrules (talk) 20:51, 27 February 2008 (UTC)

A third definition?

I don't understand the point of the newly added "solid-state physics definition". It looks the same as the physics definition to me. Dicklyon (talk) 05:07, 22 May 2012 (UTC)

I can see the purpose of the section if it is put somewhere else in the article and cut down to one or two sentences. Something like...

In solid-state physics, the "wavevector" of an electron wavefunction is conventionally given by the physics definition. These electron waves are not ordinary sinusoidal waves, but they do have a kind of envelope function which is sinusoidal, and the wavevector is defined via that envelope wave. See Bloch wave for further details.

--Steve (talk) 04:29, 23 May 2012 (UTC)

If that was the point, i totally missed it. Would you be willing to fix it per your suggestion? Dicklyon (talk) 06:36, 23 May 2012 (UTC)

Done. Hope that's OK with everyone... --Steve (talk) 14:55, 23 May 2012 (UTC)

Yes, but also in crystals, one often uses the crystal momentum, $\hbar \mathbf {k}$, in the reduced zone scheme. Since the math is periodic in the reciprocal lattice vectors, one can reduce the vector to the first Brilloin zone. (Except for calculations that need the extended zone scheme.) Gah4 (talk) 07:22, 7 April 2018 (UTC)

wave vector, direction of propagation, energy flow

I'm confused, that the article says the direction of propagation and the energy flow are equivalent.

The article arguments then (it begins in the introduction) that the wave vector does not always indicate the propagation direction of the wave.

Until today I thought it's the opposite:

The wave vector indicate always the direction of the propagation, but the direction of the propagation and the energy flow (indicated by the Poynting vector) can be different.

Short version:

actually the article says: energyflow = direction of propagation ≠ wave vector

I think it should be: energyflow ≠ direction of propagation = wave vector

--Verrain (talk) 09:24, 25 April 2018 (UTC)

There is phase velocity and group velocity, which can be in different directions. Gah4 (talk) 18:10, 6 August 2020 (UTC)

relativity

In the special relativity section, all have the K on the left, except four-momentum which has P on the left. Would it be more consistent to arrange with the K on the left? Gah4 (talk) 18:12, 6 August 2020 (UTC)

Harmonize symbols with wavenumber

I will be making several edits here to harmonize the symbols with wavenumber. Frowns will be replaced with tildas. Constant314 (talk) 00:49, 8 May 2023 (UTC)