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

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Experiments explained:

spontaneous emission coefficients.
fine structure, notably for example Dirac equation solution for the hydrogen atom
antimatter
particle creation and annihilation

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Experiments not explained: those that quantum electrodynamics explains like:

Lamb shift
TODO: quantization of the electromagnetic field as photons?

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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 64. ""Quantum Mechanics 12a - Dirac Equation I" by ViaScience (2015)" at https://youtu.be/OCuaBmAzqek?t=1010:

Equation 30. Expanded Dirac equation in Planck units.

i \partial_{t} ⎣ ⎢ ⎢ ⎢ ⎡ ψ_{1} ψ_{2} ψ_{3} ψ_{4} ⎦ ⎥ ⎥ ⎥ ⎤ = - i \partial_{x} ⎣ ⎢ ⎢ ⎢ ⎡ ψ_{4} ψ_{3} ψ_{2} ψ_{1} ⎦ ⎥ ⎥ ⎥ ⎤ + \partial_{y} ⎣ ⎢ ⎢ ⎢ ⎡ - ψ_{4} ψ_{3} - ψ_{2} ψ_{1} ⎦ ⎥ ⎥ ⎥ ⎤ - i \partial_{z} ⎣ ⎢ ⎢ ⎢ ⎡ ψ_{3} - ψ_{4} ψ_{1} - ψ_{2} ⎦ ⎥ ⎥ ⎥ ⎤ + m ⎣ ⎢ ⎢ ⎢ ⎡ ψ_{1} ψ_{2} - ψ_{3} - ψ_{4} ⎦ ⎥ ⎥ ⎥ ⎤

(30)

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.

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Video 64. "Quantum Mechanics 12a - Dirac Equation I" by ViaScience (2015) Source.

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Video 65. "PHYS 485 Lecture 14: The Dirac Equation" by Roger Moore (2016) Source.

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Table of contents | 325, 2k, 28
- 1. Spontaneous emission | 85 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 2. The Dirac equation predicts spin | 10 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 3. Antimatter | 43 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 4. Particle creation and annihilation | 131, 155, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 4.1. Particle decay | 12, 12, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Particle creation and annihilation"
    - 4.1.1. Pair production | 🔗 link | 🗖 nosplit | ↑ parent "Particle decay"
  - 4.2. Relativistic particle in a box thought experiment | 12 | 🔗 link | 🗖 nosplit | ↑ parent "Particle creation and annihilation"
- 5. The Dirac equation is consistent with special relativity | 8 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 6. Derivation of the Dirac equation | 44 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 7. Pauli equation | 9 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 8. Klein-Gordon equation | 190, 443, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 8.1. Derivation of the Klein-Gordon | 253 | 🔗 link | 🗖 nosplit | ↑ parent "Klein-Gordon equation"
- 9. Solutions of the Dirac equation | 112, 227, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 9.1. Dirac equation solution for the hydrogen atom | 115 | 🔗 link | 🗖 nosplit | ↑ parent "Solutions of the Dirac equation"
- 10. Spin (physics) | 227, 551, 12 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 10.1. Spin experiments | 46, 86, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
    - 10.1.1. Stern-Gerlach experiment | 40 | 🔗 link | 🗖 nosplit | ↑ parent "Spin experiments"
    - 10.1.2. Spintronics | 0, 0, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Spin experiments"
      - 10.1.2.1. Giant magnetoresistance | 🔗 link | 🗖 nosplit | ↑ parent "Spintronics"
  - 10.2. Spin number of a field | 28, 102, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
    - 10.2.1. Why is the spin of the electron half? | 74 | 🔗 link | 🗖 nosplit | ↑ parent "Spin number of a field"
  - 10.3. Pauli exclusion principle | 80, 108, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
    - 10.3.1. Fermion | 0, 0, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Pauli exclusion principle"
      - 10.3.1.1. Boson | 🔗 link | 🗖 nosplit | ↑ parent "Fermion"
    - 10.3.2. Spin-statistics theorem | 28 | 🔗 link | 🗖 nosplit | ↑ parent "Pauli exclusion principle"
    - 10.3.3. Electron degeneracy pressure | 🔗 link | 🗖 nosplit | ↑ parent "Pauli exclusion principle"
  - 10.4. Nuclear spin | 28 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
- 11. Dirac Lagrangian | 2 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"

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Ancestors

Relativistic quantum mechanics | 95, 8k, 110
Quantum mechanics | 170, 14k, 189
Particle physics | 135, 22k, 336
Physics | 276, 29k, 500
Natural science | 0, 37k, 827
Science | 0, 41k, 938
Ciro Santilli's Homepage | 238, 154k, 2k

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Incoming links

Antimatter | 43
Derivation of the Klein-Gordon | 253
Derivation of the quantum electrodynamics Lagrangian | 267
Dirac equation | 325, 2k, 28
Dirac equation solution for the hydrogen atom | 115
Dirac equation vs quantum electrodynamics | 123
Fine structure | 60
Hyperfine structure | 68
Klein-Gordon equation | 190, 443, 1
Lamb shift | 462, 597, 1
Mathematical formulation of quantum field theory | 115, 1k, 17
Mathematical formulation of quantum mechanics | 423, 657, 5
Particle creation and annihilation | 131, 155, 3
Particle physics | 135, 22k, 336
Paul Dirac | 59
Quantum electrodynamics | 640, 3k, 19
Quantum electrodynamics experiments | 46, 264, 4
Quantum mechanics | 170, 14k, 189
Quantum physics by Jim Branson (2003) | 25
Relativistic quantum mechanics | 95, 8k, 110
Schrodinger equation | 167, 3k, 38
Solutions of the Schrodinger equation for two electrons | 166
Spectral line | 139, 566, 7
Spin | 227, 551, 12
Spontaneous emission | 85
What does it mean that photons are force carriers for electromagnetism? | 375
Why is the spin of the electron half? | 74