# What is this equation used for? $\gamma^\mu(i\partial_\mu-eA_\mu)\psi=m\psi$

As perhaps a mathematical scavenger hunt, my mother (knowing my interest in physics and math equations), sent me this image out of curiosity for what it was.

Here is the same equation taken from the image:

$$\gamma^\mu(i\partial_\mu-eA_\mu)\psi=m\psi$$

I've attempted to reverse image search it to no avail. With it's resemblance to the Schrödinger equation, I assume it lies within the realms of physics, as for why I've asked this here, rather than math.stackexhcange.

Is anyone familiar with it?

Edit: I don't know where the image is from either.

It looks like the Schrodinger equation because it is the interacting Dirac equation. Dirac discovered the Dirac equation as a relativistic Schrodinger equation. $$(i\gamma^\mu\partial_\mu - m)\psi = 0.$$ He added the electric field $$A_\mu$$, finding an equation which perfectly (to experimental accuracy) models the electron in an electromagnetic field. The prediction for the gyromagnetic moment agrees with observation to one part in $$10^{12}$$.
• 1. $A_\mu$ is not the electric field, it is the 4-potential whose derivatives give rise to the electric field. 2. The gyromagnetic moment agreeing to one part in $10^{12}$ is a result of quantisation applied to the Dirac equation - on its own it does not achieve that precision. Jul 1, 2020 at 9:17