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Mathematics for Physics

115 Electromagnetic Radiation

A self-propagating wave of electric and magnetic fields that is used to carry energy, momentum, and angular momentum away from an accelerating charge or from an atomic jump.

The photon as a radiation quantum. In quantum mechanics a quantum of radiation is a photon of energy \(hf\) and momentum \(h/\lambda\). This principle is used to treat a light beam as a stream of photons.

The photon energy and momentum are

\[ E = hf,\qquad p = \dfrac{h}{\lambda} \]

where

  • \(E\) is the photon energy.
  • \(p\) is the photon momentum.
  • \(h\) is Planck’s constant.
  • \(f\) is the frequency.
  • \(\lambda\) is the wavelength.

The Bohr frequency condition. An atom emits or absorbs a photon when it jumps between two levels whose energy difference equals \(hf\). This principle is used to match radiation to atomic spectra.

Stimulated processes. The radiation field can stimulate emission as well as absorption. This principle is used to describe lasers and thermal radiation.

115.1 References

  1. Griffiths, D. J. Introduction to Electrodynamics. Cambridge University Press, 2024. — electromagnetic radiation.
  2. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — photons.