Dirac equation

The Dirac equation is the relativistic equation of motion for a spin-one-half Dirac field, $(i{\gamma }^{\mu }{\partial }_{\mu }-m)\psi =0$, in units $\hslash =c=1$. The gamma matrices obey the Clifford algebra, ensuring that each component also obeys the free Klein-Gordon equation.

Being first order in time allows an initial spinor to determine its subsequent free evolution. The components encode spin as well as particle and antiparticle solutions; quantization interprets both kinds of excitation with positive physical energy. Coupling through the gauge covariant derivative describes an electron interacting with an electromagnetic field. The nonrelativistic limit contains the coupling of spin to a magnetic field, explaining why a scalar relativistic wave equation alone cannot describe an electron.

Adds special relativity to the Schrödinger equation, and the following conclusions come basically as a direct consequence of this!

Experiments explained:

Experiments not explained: those that quantum electrodynamics explains like:See also: Dirac equation vs quantum electrodynamics.

The Dirac equation is a set of 4 partial differential equations on 4 complex valued wave functions. The full explicit form in Planck units is shown e.g. in Video 1. "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=1010:Then as done at physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600 from why are complex numbers used in the Schrodinger equation?, we could further split those equations up into a system of 8 equations on 8 real-valued functions.