Talk:Wavenumber

The name of it

I do not agree with the "word" "wavenumber". I think that it ought to be "wave-number" all the way through. The English language does not create new compound words willy-nilly. It is not German.

"Wavenumber" is the established and official name. The word has been around for ages. It isn't up to Wikipedia to decide what to call things. If you don't like a word, take it up with the Queen.199.212.11.110 (talk) 18:41, 10 February 2010 (UTC)

As far as I know, many other wave--- aren't yet words, but wavenumber might be. Is it in the OED? Gah4 (talk) 20:08, 5 April 2018 (UTC)

It seems that this came up in a recent edit and reversion, but I don't know that it has been answered yet. Is there a WP:RS for the single word form? Gah4 (talk) 22:22, 29 November 2021 (UTC)

Jackson, Harrington, and Griffiths all use two words without a hyphen. I did not see any that wrote it as one word or a hyphenate word. I am convinced. If you want to revert my revert, then go ahead. Constant314 (talk) 22:31, 29 November 2021 (UTC)

I reverted my revert, but there are still 39 other occurrences of "wavenumber" in the article. Constant314 (talk) 22:36, 29 November 2021 (UTC)

I ran into this some years ago in a paper, where I had wavefunction and the reviewers didn't like it. Some (different) year ago, I fixed the wavefunctions in WP. I suspect that there are still plenty of wavenumber and wavevector, but I didn't count them. I think we should also rename this article (with redirect). Gah4 (talk) 01:14, 30 November 2021 (UTC)

I think this has a very certain answer. As to myself, I cannot remember seeing anything but "wavenumber" in any contemporary scientific text on spectroscopy. Evgeny (talk) 09:03, 30 November 2021 (UTC)

While "wave number" clearly exists in some fields, that ngram is pretty convincing. Also, both NIST and BIPM have "wavenumber" in their tables of derived SI units. SpinningSpark 14:11, 30 November 2021 (UTC)

I tend to still believe the OED, which I believe this uses, to indicate that it isn't (yet) an English word. I suspect wavenumber earlier than wavevector or wavefunction, though. Gah4 (talk) 16:18, 30 November 2021 (UTC)

And here you can observe how the original "wave number" has gradually changed through years to "wave-number" and then to "wavenumber" in the quoted refs... Evgeny (talk) 16:43, 30 November 2021 (UTC)

Much as I respect the OED (and frequently refer to it in discussions), I don't think we should consider any dictionary to be the final arbiter of our article titles. After all, dictionaries are supposed to report word usage, not to set the rules of word usage. Clearly in this case, they have not fully reported current usage as demonstrably shown by the ngram. SpinningSpark 22:27, 30 November 2021 (UTC)

It seems that the OED adds new words every month]. I don't know how long it takes from when it starts to be generally used, though. Note that this discussion dates to 2010. I don't know ngram well enough, especially what sampling they use. Is it representative of WP:RSs? Gah4 (talk) 01:07, 1 December 2021 (UTC)

In general, the OED ignores the separate word/hyphenation/compound word issue. They are all treated as a single entry (note that "wavenumber" redirects to "wave number"). I don't expect that wavenumber will ever have a separate entry, although they could conceivably change the headword at some point in the future.

On gbook ngrams and RS, the answer is certainly no. The ngram app is more concerned with word usage in the wild rather than accurate encyclopaedic information. They choose a set of books randomly from their scanned books with an equal number for each year. They reject books with poor OCR, but there is no other test of quality. There is, however, the facility to select which corpus of books is used – for instance American English or British English if you are interested in American/British differences. One of the corpora is "English fiction", so in principle we can get an ngram for non-fiction which hopefully would be mostly RS. It is possible to get an ngram of one ngram subtracted from another using the advanced features (more information here) but as far as I can see, the two ngrams must both be from the same corpus. It could be manually plotted quite easily, but taking a quick look, it wouldn't make a great deal of difference. The fiction corpus mostly uses "wave number", but the occurences are so low it is not going to affect the overall results significantly. SpinningSpark 15:39, 1 December 2021 (UTC)

Angular Wavenumber

I've seen the quantitiy "circular wavenumber" referred to as "angular wavenumber". "Angular" seems to be a bit more descriptive and follows the pattern of "angular frequency". (No one says "circular frequency", but language is not always symmetrical or sensible.) Also, Google finds more pages with "angular wavenumber" than "circular wavenumber". Should we retitle the "circular wavenumber" section and mention both quantity names? Zeroparallax 10:54, 17 March 2006 (UTC)

I think so, that sounds very reasonable. Fresheneesz 06:49, 8 May 2006 (UTC)

Other equation (concerning matter waves)

The solutions to a physics HW we had involved what it called the "wavenumber" "k", and it said that:

$k={\sqrt {2mE/\hbar }}$

Does this correspond with anything? I can't find anything about that formula anywhere, and our physics teacher didn't actually teach it to us, although I guess he thinks he did. That and I can't get it to reconcile with de Broiglie's relations. Anyone have any idea what he's talking about? Fresheneesz 06:49, 8 May 2006 (UTC)

If the hbar goes outside the sqrt, then that's the k you get when solving the 1-D Schrödinger equation, for the particle in a box. If you do dimensional analysis on the solution sin(kx), k must have units of inverse length, like the first paragraph says. - mako 11:38, 8 May 2006 (UTC)

Ahh, alright thanks. Do you think that in any way belongs on this page? Fresheneesz 00:30, 9 May 2006 (UTC)

I dunno. sin(kx) comes up a lot, but it doesn't strike me as a particularly important usage of the term. - mako 21:07, 9 May 2006 (UTC)

In summary, the correct relationship is:

$k={\frac {\sqrt {2mE}}{\hbar }}.$

This relationship defines the angular wavenumber of a matter wave (for example an electron) in terms of its mass, its kinetic energy, and Planck's constant (divided by 2 pi). Another correct relationship is:

$k={\frac {p}{\hbar }}.$

This relationship defines the angular wavenumber of a matter wave in terms of its momentum and Planck's constant (divided by 2 pi). These relationships hold true for a particle in a box (quantized angular wavenumbers) or free particle (continuous angular wavenumbers) because they simply restate the de Broiglie's relations. In fact the page on de Broiglie's relations refers to this article on wavenumber. Therefore the wavenumber article should refer to de Broiglie's relations. The field is quantum mechanics. --John David Wright 22:29, 23 February 2007 (UTC)

Conversion

This page need to specify the conversion factors between wavenumbers (cm-1) and Energy/angular frequency, preferably in terms of fundamental constants if that is possible. —Preceding unsigned comment added by 82.35.34.20 (talk • contribs)

Done. Han-Kwang 15:16, 4 May 2007 (UTC)

Obscurantism

It would be easier to understand the concept if we use plain language appropriate to an encyclopedia. I suggest replacing:

Wavenumber in most physical sciences is a wave property inversely related to wavelength, having SI units of reciprocal meters (m−1).

With:

Wavenumber in most physical sciences is a wave property inversely related to wavelength, having SI units of cycles per unit length or radians per unit length, where the unit length is stated and is typically meters, centimeters, nanometers etc. The dimensions are L^-1.

Also:

"The energy corresponds to a wavenumber of 300 reciprocal centimeters (or inverse centimeters or per centimeter)"

would be more clearly: "The energy corresponds to a wavenumber of 300 cycles per centimeter"

Any comments? GilesW (talk) 07:30, 22 April 2009 (UTC)

Agreed! To mere mortals (indeed, even to mortals with some physics background) it fails to give a feel for what the concept is, or to give the reader a way of envisaging it. I'll attempt a little reworking. The lead should attempt to explain to a novice the overall idea, so I'll add a sentence there to that effect. Equally the lead should avoid being overloaded with technical detail, so I'll move some of its mathematical detail down into the article itself. Feline Hymnic (talk) 22:29, 12 October 2012 (UTC)

Radial wavenumber

In the context of RF coils etc., please define "radial wavenumber". It is said to be "all important" [[1]], (see second page between expressions (3) and (4)). I cannot find a definition. GilesW (talk) 07:56, 8 May 2009 (UTC)

Spectroscopy an "oddball field"?

In this edit, physicist User:Dicklyon threw the whole article around, calling spectroscopy an oddball field. But to hosts of chemists and biologists, wavenumbers has no other meaning than a unit of energy. The lead of this article now ignores that. It only explains this term as angular wavenumber, which is the magnitude of the wave vector, of relevance only to physicists that should already know what this is anyway. The article should aim at the general reader, which is someone who wants to know what it means that a "Raman peak is at 300 wavenumbers". /Pieter Kuiper (talk) 07:41, 24 March 2010 (UTC)

By "oddball" I only meant that it's the minority usage, unique to that field, as opposed to all the fields where wavenumber means what you're calling angular wavenumber. Integrate the alternative into the lead if you like, but don't make it dominate the usual meaning. Dicklyon (talk) 23:48, 24 March 2010 (UTC)

A search like http://www.google.se/search?q=wavenumbers shows that the term is most often used to denote a unit of energy. For chemists and biologists, it is the meaning that they will usually encounter. Look at how common it is to speak of "Raman wavenumbers" or "vibrational wavenumbers". /Pieter Kuiper (talk) 00:07, 25 March 2010 (UTC)

I agree with the 2nd sentiment. I am a chemist, and so I fully understand your frustration looking for the term you expect to be described on wikipedia directly and finding this article. I have looked at plenty of IR/Raman spectra... that being said defining wavenumber in this sense as anything other than a highly SPECIFIC and NONSTANDARD or otherwise SPECIALIZED application of the term, and one that is actually "set" to an implicitly agreed upon metric (eg the typical absorption energies of IR and Raman vibronic states of commonly encountered materials, the most common in educational settings being carbon-heteroatom bonds... inverse centimeters) would be misleading at best and outright false at worst. It would be like arguing that the article for "Parts per million" does not include the frequency shift measurement used practically in nuclear magnetic resonance spectroscopy (NMR)... just because chemists and biochemists are used to referring to this shift as "PPM" does not mean that the term is even remotely common outside of these fields, and is still more often used for concentration or density even IN those fields. In terms of Raman and IR, it would be just as valid to refer to the absorption energies in joules but it is common practice to use inverse centimeters or "wavenumbers" in educational and applicable literature (eg the highly highly specialized synthetic organic chemistry literature). It should be said that there are plenty of physical chemists, materials scientists, and theoretical/computational chemists that use the term "wavenumber" in its more standard physical meaning.2602:306:CE95:5230:A189:95B8:C7E8:546E (talk) 06:26, 22 July 2017 (UTC)

I was about to make a new comment related to theoretical physics, which seems to contrast with spectroscopy. It seems to me that all physics other than spectroscopy using k, or angular wave number, often enough wave vector. This is even true, and it often is, then the actual subject is optical spectrum. Well, more along with hbar in relation to quantum mechanics, or at least photons. So, yes, as a subfield of physics, it seems that spectroscopy is the oddball. Partly this traces back to the beginning, before the speed of light was accurately measured (and before it was defined), wavelength can be determined from diffraction gratings. All the math works better without so many 2pi around. Gah4 (talk) 21:05, 17 January 2021 (UTC)

Energy vs frequency

This edit:

http://en.wikipedia.org/w/index.php?title=Wavenumber&diff=prev&oldid=33599618

seems inconsistent with $E=h\nu =\hbar \omega$. The equation, as it presently appears, is:

$k\equiv {\frac {2\pi }{\lambda }}={\frac {2\pi \nu }{v_{p}}}={\frac {\omega }{v_{p}}}={\frac {E}{\hbar c}},$

but should (I think) be:

$k\equiv {\frac {2\pi }{\lambda }}={\frac {2\pi \nu }{v_{p}}}={\frac {\omega }{v_{p}}}={\frac {E}{\hbar v_{p}}}.$

Comments? —Preceding unsigned comment added by 70.234.243.222 (talk) 02:14, 11 April 2010 (UTC)

See also

I was curious as to what the connection is between wave number and curvature. Why would you have a reference to curvature on this page? —Preceding unsigned comment added by 65.199.189.6 (talk) 15:02, 14 July 2010 (UTC)

Other than because wavenumber and curvature both have dimensions of inverse length, I can't think of a relation. Miguel (talk) 08:31, 15 April 2013 (UTC)

Sounds a reasonable question. The curvature article doesn't mention wavenumber, so there's no obvious link. I'll remove the this "see also" item. Feline Hymnic (talk) 22:34, 12 October 2012 (UTC)

wavenumber / energy equivalence in other medium besides vacuum?

"For electromagnetic radiation in vacuum, wavenumber is proportional to frequency and to photon energy." Ok so what about if we're not in vacuum? Apparently when a photon goes from vacuum (index of refraction 1.0) to glass (index of refraction 1.5) the wavenumber would increase by the same amount (1.5 divided by 1.0). Does that imply its energy increased by the same amount? And when it leaves the glass would it lose that energy?

I can't find answers to these questions anywhere on the internet. Odd...

24.162.242.96 (talk) 13:32, 14 June 2013 (UTC)

Wave vector

The content of this article is largely redundant with the article Wave vector, and would be even more if that article were as well written as this. Wouldn't it be clearer if the two articles were merged? 85.23.38.101 (talk) 17:34, 2 March 2014 (UTC)

Wave vector pretty reliably uses the radian definition: $k=2\pi /\lambda$. I am not so sure about wave number, which is otherwise the magnitude of a wave vector. That is needed so that $\psi (x,t)=A\cos(kx-\omega t+\varphi )$ works. Gah4 (talk) 01:09, 30 November 2021 (UTC)

Complex

Why is permeability μ₀ mentioned in this article? Simon de Danser (talk) 08:48, 23 November 2016 (UTC)

In theory you need actual permeability, but there aren't so many transparent ferromagnetic materials, so mostly it is needed for unit conversion. All works better in CGS units. Gah4 (talk) 20:57, 17 January 2021 (UTC)

Inverse dependence of the energy of the wavenumber

In the introduction it is currently written

"1 cm−1 of energy is the amount of energy in a single photon with a wavelength of 1 cm"

This seems to imply a linear connection between wavenumber and energy, which is however inverse. I would change it into:

"10 cm−1 of energy is the amount of energy in a single photon with a wavelength of 1/10 cm"

Thoughts?

Further I suggest to link a energy converter, like this one:

[2]

130.83.182.68 (talk) 14:41, 15 February 2017 (UTC)

There is a linear dependence between energy and wavenumber. That is, increased wavenumber corresponds to increased photon energy. Gah4 (talk) 20:18, 5 April 2018 (UTC)

In optical spectroscopy, it is often used as a unit of temporal frequency assuming a certain speed of light.

As well as I know it, wavenumber was used in spectroscopy from the days before an accurate speed of light. Wavenumber can be directly measured with a diffraction grating, so it is more like temporal frequency can be determined from wavenumber, assuming a certain speed of light. Gah4 (talk) 20:16, 5 April 2018 (UTC)

I was about to write this again, but I see that I already did. Any thoughts since last year? Gah4 (talk) 03:47, 10 June 2019 (UTC)

Remove Definition section.

I suggest removing the 'Definition' section entirely as there are two inconsistent definitions of wavenumber and the current section is mixed up between them. Instead let's just have the two sections "In wave equations" and "In spectroscopy" that each address their own internally consistent logic.

Wavenumber definition 1 (general wave equations):

• A measure of waves per unit length, i.e., the inverse of wavelength.
• Units can be anything that is inverse of length (1/m, 1/cm, 1/micron, 1/nm)
• Changes when a wave propagates into a different medium (red light has 1.6 μm^-1 wavenumber in air; red light has 2.1 μm^-1 wavenumber in water).
• Can be complex.

Wavenumber definition 2 (spectroscopy):

• A measure of energy quantum as scaled by $hc$ (e.g., "The spacing between the two orbitals is 50 cm^-1.").
• A measure of frequency as scaled by $c$ (e.g., "The laser has bandwidth of 10 cm^-1").
• Units are typically inverse centimeter (cm^-1), also called "wavenumbers" in speech (e.g., "The energy levels are spaced by 50 wavenumbers.").
• Does not change when a light wave propagates into a different medium (an atom emitting red light emits light with wavenumber ~16000 cm^-1 regardless of whether it's in diamond or vacuum)
• In other words, it only equals the inverse of wavelength for the special case of light waves in vacuum.
• Seems to be always real-valued.

Thoughts? --Nanite (talk) 22:06, 5 April 2018 (UTC)

No comment on removing or not the definition section. The conversion is $hc$ for spectroscopy wavenumber and ${\hbar }c$ for radians/length. I am not sure how spectroscopists consider the index of refraction. I will guess that they correct for it. Monochromators are usual in air, and not other media. Physics uses $k$ in wave equations, and that could be in any media. Gah4 (talk) 03:47, 6 April 2018 (UTC)

Ah thanks, you are right on the factor of c being inverted -- I've corrected my post. --Nanite (talk) 19:29, 6 April 2018 (UTC)

This is one of those "you know it when you see it, but otherwise it is hard to explain" cases. I believe that spectroscopists use it in place of frequency, from the early days before there were good measurements of c. From a diffraction grating, you measure wavelength but not frequency. Many equations in spectroscopy work better with a quantity that is inverse wavelength, especially in diffraction. Otherwise in QM the quantity that you want is the one that goes with $\omega$, and so should not change with index of refraction. As you note, it is energy with $hc$ factored out. Gah4 (talk) 19:59, 6 April 2018 (UTC)

In physics, wave vector is commonly used, especially in the form $e^{i({\mathbf {k\cdot x} }-\omega t)}$. First, this $\mathbf {k}$ is $2\pi$ times the form used by spectroscopists, but also is a vector. However, the non-vector $k$ might be used for the magnitude of the vector. In this form, it is used for the solution of wave equations, where it describes the spatial part of propagating waves. Also, in absorbing materials it is complex. The imaginary component, along with the i in the exponent, forms a decreasing exponential. My first thought is that this is not called a wave number, maybe magnitude of wave vector, but I am not yet convinced of that. Then the phase velocity of a wave is $\omega /k$ and the group velocity $d\omega /dk$, again these can be complex. Gah4 (talk) 19:59, 6 April 2018 (UTC)

historical

As far as I know, the historical reason for spectroscopy to use wavenumber instead of frequency is that measurements were already more accurate than the known speed of light. In many places, such as acoustics, it is easier to describe waves in terms of frequency, but that wasn't the case here. Only later when the connection through quantum mechanics to photon energy came about, did this distinction become important. Gah4 (talk) 13:54, 31 October 2018 (UTC)

"Orders of magnitude (wavenumber)" listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Orders of magnitude (wavenumber). Please participate in the redirect discussion if you wish to do so. Utopes _{(talk / cont)} 22:54, 7 April 2020 (UTC)