Talk:Wavenumber

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[edit] 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)

[edit] 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{2 m E / \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{2 m E }}{\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)

[edit] 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)