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

Experiments explained:

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

Experiments not explained: those that quantum electrodynamics explains like:See also: Dirac equation vs quantum electrodynamics.

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

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

$i∂_{t}⎣⎢⎢⎢⎡ ψ_{1}ψ_{2}ψ_{3}ψ_{4} ⎦⎥⎥⎥⎤ =−i∂_{x}⎣⎢⎢⎢⎡ ψ_{4}ψ_{3}ψ_{2}ψ_{1} ⎦⎥⎥⎥⎤ +∂_{y}⎣⎢⎢⎢⎡ −ψ_{4}ψ_{3}−ψ_{2}ψ_{1} ⎦⎥⎥⎥⎤ −i∂_{z}⎣⎢⎢⎢⎡ ψ_{3}−ψ_{4}ψ_{1}−ψ_{2} ⎦⎥⎥⎥⎤ +m⎣⎢⎢⎢⎡ ψ_{1}ψ_{2}−ψ_{3}−ψ_{4} ⎦⎥⎥⎥⎤ $

## Tagged

## Ancestors

## Incoming links

- Antimatter
- Derivation of the Dirac equation
- Derivation of the Klein-Gordon equation
- Derivation of the quantum electrodynamics Lagrangian
- Dirac equation
- Dirac equation solution for the hydrogen atom
- Dirac equation vs quantum electrodynamics
- Dirac Lagrangian
- Fine structure
- Hyperfine structure
- Internal and spacetime symmetries
- Klein-Gordon equation
- Lamb-Retherford experiment
- Lamb shift
- Mathematical formulation of quantum field theory
- Particle creation and annihilation
- Particle physics
- Paul Dirac
- Quantum electrodynamics
- Quantum electrodynamics experiment
- Quantum mechanics
- Quantum physics by Jim Branson (2003)
- Relativistic quantum mechanics
- Schrödinger equation
- Schrödinger picture
- Solutions of the Schrodinger equation for two electrons
- Spectral line
- Spin half
- Spin
- Spontaneous emission
- What does it mean that photons are force carriers for electromagnetism?
- Why is the spin of the electron half?