# Showing the annihilation of an electron-positron pair [duplicate]

How to show that the annihilation of an electron-positron pair under emission of one real photon (mass zero) is forbidden by energy-momentum conservation, the emission of two photons is allowed?

• I know the linked duplicate asks for $\gamma\to e^+ e^-$ instead of $e^+ e^-\to\gamma$, but that doesn't make a difference for the answer. – ACuriousMind Jan 25 '16 at 22:27

Obviously, there exists no one-photon system with positive energy which has 0 momentum, as the energy-momentum relation for a photon is $E = p c$.
• @user83866 $p=\frac{E}{c}$ for a single photon cannot equal 0, but $p_{epcm}=0$. That's the math. – Bill N Jan 25 '16 at 22:43