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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:
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 https://youtu.be/OCuaBmAzqek?t=1010:
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.
Video 1. Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015) Source.
Video 2. PHYS 485 Lecture 14: The Dirac Equation by Roger Moore (2016) Source.

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