Dirac equation

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Adds special relativity to the Schrödinger 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 73. ""Quantum Mechanics 12a - Dirac Equation I" by ViaScience (2015)" at https://youtu.be/OCuaBmAzqek?t=1010:

Equation 48. 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} ⎦ ⎥ ⎥ ⎥ ⎤

(48)

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

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Video 74. "PHYS 485 Lecture 14: The Dirac Equation" by Roger Moore (2016) Source.

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Table of contents | 329, 2k, 38
- 1. Spontaneous emission | 91 | 🔗 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 | 133, 157, 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 | 51 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 7. Pauli equation | 11 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 8. Klein-Gordon equation | 243, 496, 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 | 120, 236, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 9.1. Dirac equation solution for the hydrogen atom | 116 | 🔗 link | 🗖 nosplit | ↑ parent "Solutions of the Dirac equation"
- 10. Spin (physics) | 229, 866, 19 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 10.1. Spin experiments | 101, 172, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
    - 10.1.1. Stern-Gerlach experiment (1921) | 42 | 🔗 link | 🗖 nosplit | ↑ parent "Spin experiments"
    - 10.1.2. Spintronics | 0, 29, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Spin experiments"
      - 10.1.2.1. Tunnel magnetoresistance | 29 | 🔗 link | 🗖 nosplit | ↑ parent "Spintronics"
      - 10.1.2.2. Giant magnetoresistance | 🔗 link | 🗖 nosplit | ↑ parent "Spintronics"
  - 10.2. Spin number of a field | 37, 115, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
    - 10.2.1. Why is the spin of the electron half? | 78 | 🔗 link | 🗖 nosplit | ↑ parent "Spin number of a field"
  - 10.3. Pauli exclusion principle | 102, 132, 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 | 30 | 🔗 link | 🗖 nosplit | ↑ parent "Pauli exclusion principle"
    - 10.3.3. Electron degeneracy pressure | 🔗 link | 🗖 nosplit | ↑ parent "Pauli exclusion principle"
  - 10.4. Nuclear spin | 30 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
  - 10.5. Spin comes naturally when adding relativity to quantum mechanics | 140, 188, 5 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
- 11. Dirac Lagrangian | 136, 136, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"

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Ancestors

Relativistic quantum mechanics | 99, 10k, 149
Quantum mechanics | 169, 20k, 270
Particle physics | 137, 32k, 512
Physics | 276, 46k, 825
Natural science | 0, 61k, 2k
Science | 0, 66k, 2k
Ciro Santilli's Homepage | 262, 218k, 4k

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Incoming links

Antimatter | 43
Derivation of the Dirac equation | 51
Derivation of the Klein-Gordon | 253
Derivation of the quantum electrodynamics Lagrangian | 274
Dirac equation | 329, 2k, 38
Dirac equation solution for the hydrogen atom | 116
Dirac equation vs quantum electrodynamics | 151
Dirac Lagrangian | 136, 136, 3
Fine structure | 60, 208, 2
Hyperfine structure | 148
Internal and spacetime symmetries | 287, 287, 2
Klein-Gordon equation | 243, 496, 1
Lamb-Retherford experiment | 301
Lamb shift | 516, 817, 1
Mathematical formulation of quantum field theory | 251, 1k, 18
Mathematical formulation of quantum mechanics | 490, 1k, 6
Particle creation and annihilation | 133, 157, 3
Particle physics | 137, 32k, 512
Paul Dirac | 477
Quantum electrodynamics | 683, 3k, 29
Quantum electrodynamics experiments | 46, 360, 5
Quantum mechanics | 169, 20k, 270
Quantum physics by Jim Branson (2003) | 27
Relativistic quantum mechanics | 99, 10k, 149
Schrödinger equation | 555, 5k, 60
Solutions of the Schrodinger equation for two electrons | 230
Spectral line | 165, 1k, 11
Spin half | 11
Spin | 229, 866, 19
Spontaneous emission | 91
What does it mean that photons are force carriers for electromagnetism? | 385
Why is the spin of the electron half? | 78