# What is wavenumber: Definition and 30 Discussions

In the physical sciences, the wavenumber (also wave number or repetency) is the spatial frequency of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (ordinary frequency) or radians per unit time (angular frequency).
In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck's constant is the canonical momentum.
Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy, it is often used as a unit of temporal frequency assuming a certain speed of light.

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1. ### B What do these wavenumbers correspond to in Raman spectroscopy?

I don't know whether it is an energy of a photon emitted by a deexciting molecule, or if it is an energy of laser's photons. Here is an example of such spectrum: For example, that value of wavenumber ##3000\, \mathrm {cm^{-1}}## is an energy of an emitted photon or a photon from laser? And that...
2. ### I Issue with wavenumber in the free particle wavefunction

To me, the ##K## obtained by solving the Schrodinger equation and the de broglie wavelength seem two completely unrelated quantities. Can someone explain why have we equated ##K## and ##\frac{2\pi}{\lambda}##. Also, isn't writing ##p = \hbar K## implying that eigenstate of energy is also an...
3. ### I Planck's law in wavenumber vs. wavelength

I have asked this question elsewhere. I have gotten no clear answer. What I already know: The interval (differential) sizes (areas) are different in terms of wavelength and wavenumber. The total energy is the same when the curves are integrated over all wavelengths or wavenumbers So please...

14. ### Exploring Wavenumber & Position Eigenstates

If the wavenumber eigenstates are |k> and the position eigenstates are |x>, then my notes say we can write |k>=∫-∞∞ek(x)|x>dx i.e express a wavenumber eigenstate in terms of a superposition of position eigenstates. Now they state that ek(x)=eikx/√(2π). I don't understand how we can say that the...
15. ### Wavenumber Units: Standard or Free-for-All?

Hi there, quick question about units. I know wavenumber can be defined as 1/λ or 2π/λ, the latter sometimes being termed 'angular' wavenumber. Is there an agreed upon way of distinguishing between these two definitions when displaying units on, for example, a graph or paper? I've seen...
16. ### Difference between wavenumber and wave mode?

Are these two, wave number and wave mode, same thing? If not, what is the difference? Thanks...
17. ### Propagation of uncertainty from wavenumber to wavelength

Hi, This is just a quick question. If wavenumber is a variable with some standard deviation Δk, how do I propagate this spread when converting from wavenumber to wavelength? Is it just 2π/Δk or is it more complex than that? Thanks
18. ### Kramers-Kronig relations for the wavenumber

Hi all, I am wandering if I can apply the Kramers-Kronig (KK) relations to the complex wavenumber k(ω) = k'(ω) + i k"(ω). I have a measurement that easily gives me k'(ω) for a certain range of frequencies, but where k"(ω) is unreliable. I would like to use KK to find k" from k'. According...
19. ### Can I have different wavenumber and frequency in E and B for a plane e

Homework Statement To solve the wave equations in vacuum for ##\vec{E}## and ##\vec{B}## we made the ansatz: \begin{array}{cc} \vec{E}\left(\vec{r},t\right)=\vec{E}_{0}\cos\left(\vec{k}\cdot\vec{r}-\omega t+\delta\right)...
20. ### Finding band origin of electronic transition and wavenumber of vibrational mode

Homework Statement The first vibrational band in the absorption spectrum of H2CO is at 28871 cm-1. The first two bands in the emission spectrum (from v'=0 level) lie at 27021 cm-1 and 24687 cm-1. Explain these observations. Determine the band origin of the electronic transition and the...
21. B

### Show that the real and imaginary parts of the wavenumber, k, are given by

Homework Statement Show that the real and imaginary parts of the wavenumber, k, are given by k(real)=[sqrt(epsilon(real))]omega/c and k(imaginary)=[epsilon(imaginary) *omega/(2c sqrt(espilon(real))) The Attempt at a Solution k^2= mu epsilon omega^2 (1+(i g/epsilon*omega)) k^2...
22. ### What is the Wavenumber and Transition for an H-Atom with n=732 to n=731?

Homework Statement Calculate a diameter of an H-atom with n=732. Calculate also the value of the wavenumber corresponding to the transition from n=732 to n=731 Homework Equations E_{trans}= \frac{-E_{h}}{(732)^2}-\frac{-E_{h}}{(731)^2}} The Attempt at a Solution...
23. ### Physical significance of wavenumber

i do not understand what is the physical significance of wavenumber. i have a plot with wavenumber on x-axis and count on the y axis. what does the plot mean, how can i relate to a practical example. please help
24. ### How to Insert Wavenumber Symbol and Draw Triple Bonds in Word?

Hi Does anyone know how to get the symbol for wavenumber, nu bar, in Word? Also if anyone has any tips on how to draw a triple bond quickly in Word. I'm happy to use the equal sign for a double bond thanks
25. ### Lenard Jones Potential & wavenumber

I was just wondering, given that you have the dispersion relation omega = omega(k) for a Lenard-Jones potential in say a monatomic crystalline solid of lattice spacing a, which is proportional to sin(ka/2) where k is the wavenumber. The group velocity is the derivative of the dispersion relation...
26. ### Planck function expressed in Wavenumber?

Homework Statement I am checking some equations for my simulation and are looking at the Planck function. My question involves the constant used for the Planck function expressed in Wavenumbers. I have found this expression for the function...
27. ### Explanation of Wavenumber wrt Turbulence and Energy dissipation

Hi there Can anyone provide me with an explanation of what a wavenumber is, and how it can be used in determining the extent to which energy is dissipated during turbulence (ideally in the context of the ocean)? I am aware of the basic definition of a wavenumber (i.e. the reciprocal of wave...
28. ### How Is Wavenumber Calculated for Large Topography Disturbances in Steady Waves?

This is an ultra vague question, but I'm hoping to bump into an expert who might know. Consider the steady flow of water over a polygonal surface (like a step, for instance -- something that can be easily conformally mapped). The wavenumber of the far field (large x) gravity waves can be found...
29. ### Sign of Wavenumber: Electromagnetic Material

Hi. In electromagnetics, a material(linear,isotropic,homogenous) with constitutive parameters \epsilon and \mu has the wavenumber k^2=\omega^2\epsilon\mu. Consequently k=\pm\omega\sqrt{\epsilon\mu}. Does this mean that \omega can actually be negative, and if so, when is it the case? It seems...
30. ### Difference in Physics and Chemistry Text regarding Wavenumber

Hi Those of you who have read Bohr's Theory in Chemistry may have encountered the relation, \frac{1}{\lambda} = RhcZ^{2}(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}) for the wavelength of radiation emitted when an electron goes from a higher energy level n_{2} to a lower energy level...