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# Dirac equation

nosplit "Relativistic quantum mechanics" words: 2k
Adds special relativity to the Schrödinger equation, and the following conclusions come basically as a direct consequence of this!
Experiments not explained: those that quantum electrodynamics explains like:
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 https://youtu.be/OCuaBmAzqek?t=1010: $$Equation 1. Expanded Dirac equation in Planck units. i∂t​⎣⎢⎢⎢⎡​ψ1​ψ2​ψ3​ψ4​​⎦⎥⎥⎥⎤​=−i∂x​⎣⎢⎢⎢⎡​ψ4​ψ3​ψ2​ψ1​​⎦⎥⎥⎥⎤​+∂y​⎣⎢⎢⎢⎡​−ψ4​ψ3​−ψ2​ψ1​​⎦⎥⎥⎥⎤​−i∂z​⎣⎢⎢⎢⎡​ψ3​−ψ4​ψ1​−ψ2​​⎦⎥⎥⎥⎤​+m⎣⎢⎢⎢⎡​ψ1​ψ2​−ψ3​−ψ4​​⎦⎥⎥⎥⎤​ (1)$$ Then as done at https://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.