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# 2.6: Quantum Theory of Light


According to Einstein’s quantum theory of light, a monochromatic light-wave of angular frequency $$\omega$$, propagating through a vacuum, can be thought of as a stream of particles, called photons, of energy

$\label{e2.17} E = \hbar\,\omega,$ where $$\hbar = h/2\pi = 1.0546\times 10^{-34}\,{\rm J\,s}$$. Because classical light-waves propagate at the fixed velocity $$c$$, it stands to reason that photons must also move at this velocity. According to Einstein’s special theory of relativity, only massless particles can move at the speed of light in vacuum . Hence, photons must be massless. Special relativity also gives the following relationship between the energy $$E$$ and the momentum $$p$$ of a massless particle , $p = \frac{E}{c}.$ Note that the previous relation is consistent with Equation (2.4.12), because if light is made up of a stream of photons, for which $$E/p=c$$, then the momentum density of light must be the energy density divided by $$c$$. It follows, from the previous two equations, that photons carry momentum $\label{e2.19b} p = \hbar\,k$ along their direction of motion, because $$\omega/c = k$$ for a light-wave. [See Equation (2.4.5).]
