# Wavelength vs Wavenumber etiquette

When am I supposed to use the terminology of EM "wavenumber", instead of "wavelength" (or frequency)?

The concepts of wavelength and frequency are no problem for me, but wavenumber (number of wavelengths per unit length) seems redundant to me as a student engineer and proto-physicist. And then there's use of energy levels at higher frequencies.

• Read this: en.wikipedia.org/wiki/Wavenumber – docscience Jul 31 '15 at 17:46
• Wavenumber is just a convenience -- it's a lot easier to write $e^{ikx}$ than it is to write $e^{2\pi i x\frac\lambda}$. And if you're writing the first thing, you need a name with which to refer to $k$. They are 100% the same thing, though. – Jerry Schirmer Jul 31 '15 at 17:46

Traditionally wavenumber is used in molecule spectrums such as infrared spectrums in organic chemistry where it is given in the incoherent SI-unit $\textrm{cm}^{-1}$. Mostly because one obtains convenient numbers on the axis. Also in most of the wave equations it is used, because again you can make the convenient substitution $k \equiv \frac{2\pi}{\lambda} = \frac{p}{\hbar}= \frac{\sqrt{2 m E }}{\hbar}$ which is commonly done in solving the Schrödinger equation for simple boundary constraints. Thus it depends on the exact context if you would use the first or latter.