Tag Info

Propagating solutions to Maxwell’s equations in classical electromagnetism and real photons in quantum electrodynamics. A superset of thermal-radiation.

## When to Use this Tag

Use this tag to discuss electromagnetic waves. Since these arise either from or , you might want to include either of these two tags as well. For high-energy physics, look at . For electromagnetic waves originating from a black body, instead use ; the photo-electric effect also has its own tag .

## Introduction

The defining property of an electromagnetic wave is its frequency $\nu$, which is related to the wavelength $\lambda$ of the wave by $c = \lambda \nu$. The electromagnetic wave propagates with the speed of light $c = \sqrt{\varepsilon_0 \mu_0 \varepsilon_r \mu_r}^{-1}$, where $\mu_r$ and $\varepsilon_r$ are material-dependent constants. The SI system defined $c_{\textrm{Vacuum}} \equiv 299\;792.458\textrm{ km/h}$. Visible light has a wavelength of $400\textrm{ nm} \lesssim \lambda \lesssim 800\textrm{ nm}$ in vacuum.

There are two main descriptions of electromagnetic waves: Classically, they can be described as propagating solutions to , that is, ‘normal‘ electromagnetic fields that change in time and position according to the electromagnetic wave equations.

However, the photoelectric effect can only be explained by quantised electromagnetic waves; waves that consist of particles carrying the energy of the wave. These particles are called photons, are massless and move at the speed of light. However, due to the energy of the electromagnetic field carried by them, a single photon has a non-zero momentum $p = h / \lambda$ and non-zero energy $E = h \nu$, with $h$ being Planck’s constant.

It is often convenient to define the angular frequency $\omega \equiv 2 \pi \nu$, the wave-number $k \equiv 2 \pi / \lambda$ and the reduced Planck’s constant $\hbar \equiv h / (2 \pi)$. We then have $p = \hbar k$ and $E = \hbar \omega$.
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