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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.

mystery equation

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.

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2 Answers 2

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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 $10^{12}$.

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  • $\begingroup$ Fascinating, thank you for elaborating $\endgroup$
    – Graviton
    Commented Jun 30, 2020 at 22:28
  • $\begingroup$ 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. $\endgroup$
    – JamalS
    Commented Jul 1, 2020 at 9:17
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It's the Dirac equation (RQM) for a fast charged particle in an EM field

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  • $\begingroup$ Just a little detail, i would specify fermion rather than a general particle $\endgroup$ Commented Jun 30, 2020 at 8:59
  • $\begingroup$ It is also written in a form that leads to a local gauge invariant Lagrangian. $\endgroup$
    – Nemo
    Commented Jun 30, 2020 at 9:41

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