Dirac equation | 🗖 nosplit | ↑ parent "Relativistic quantum mechanics" | 304, 26, 2k

🗖 nosplit | ⇓ toc | ↑ parent "Relativistic quantum mechanics" | Wikipedia | 304, 26, 2k

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 57. ""Quantum Mechanics 12a - Dirac Equation I" by ViaScience (2015-12-19)" at https://youtu.be/OCuaBmAzqek?t=1010:

Equation 25. 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} ⎦ ⎥ ⎥ ⎥ ⎤

(25)

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 57. "Quantum Mechanics 12a - Dirac Equation I" by ViaScience (2015-12-19) Source.

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Video 58. "PHYS 485 Lecture 14: The Dirac Equation" by Roger Moore published on 2016-04-07. Source.

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Table of contents | 304, 26, 2k
- 1. Spontaneous emission | 78 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 2. The Dirac equation predicts spin | 9 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 3. Antimatter | 40 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 4. Particle creation and annihilation | 127, 3, 149 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 4.1. Particle decay | 11, 1, 11 | 🔗 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 | 11 | 🔗 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 | 42 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 7. Pauli equation | 9 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
- 8. Klein-Gordon equation | 181, 1, 425 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 8.1. Derivation of the Klein-Gordon | 244 | 🔗 link | 🗖 nosplit | ↑ parent "Klein-Gordon equation"
- 9. Solutions of the Dirac equation | 101, 1, 205 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 9.1. Dirac equation solution for the hydrogen atom | 104 | 🔗 link | 🗖 nosplit | ↑ parent "Solutions of the Dirac equation"
- 10. Spin (physics) | 219, 11, 518 | 🔗 link | 🗖 nosplit | ↑ parent "Dirac equation"
  - 10.1. Spin experiments | 38, 3, 77 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
    - 10.1.1. Stern-Gerlach experiment | 39 | 🔗 link | 🗖 nosplit | ↑ parent "Spin experiments"
    - 10.1.2. Spintronics | 0, 1, 0 | 🔗 link | 🗖 nosplit | ↑ parent "Spin experiments"
      - 10.1.2.1. Giant magnetoresistance | 🔗 link | 🗖 nosplit | ↑ parent "Spintronics"
  - 10.2. Why is the spin of the electron half? | 69 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
  - 10.3. Pauli exclusion principle | 102, 4, 128 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"
    - 10.3.1. Fermion | 0, 1, 0 | 🔗 link | 🗖 nosplit | ↑ parent "Pauli exclusion principle"
      - 10.3.1.1. Boson | 🔗 link | 🗖 nosplit | ↑ parent "Fermion"
    - 10.3.2. Spin-statistics theorem | 26 | 🔗 link | 🗖 nosplit | ↑ parent "Pauli exclusion principle"
    - 10.3.3. Electron degeneracy pressure | 🔗 link | 🗖 nosplit | ↑ parent "Pauli exclusion principle"
  - 10.4. Nuclear spin | 25 | 🔗 link | 🗖 nosplit | ↑ parent "Spin"

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Dirac equation | 🗖 nosplit | ↑ parent "Relativistic quantum mechanics" | 304, 26, 2k

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