Dirac equation

The relativistic quantum wave equation for spin-1/2 particles such as electrons, describing how the wavefunction evolves in time. It combines quantum mechanics with special relativity and predicts electron spin and antimatter.

i ℏ \frac{\partial Ψ}{\partial t} = (c α^\cdot p^+ m c^{2} β^) Ψ

i\hbar\frac{\partial \Psi}{\partial t} = \left(c\hat{\boldsymbol{\alpha}}\cdot\hat{\boldsymbol{p}} + mc^2\hat{\beta}\right)\Psi

What the symbols mean

$i$	imaginary unit
$ℏ$	reduced Planck constant (J\cdot s)
$Ψ$	four-component Dirac spinor wavefunction
$t$	time (s)
$c$	speed of light in vacuum (m/s)
$α^$	vector of Dirac alpha matrices
$p^$	momentum operator (kg\cdot m/s)
$m$	rest mass of the particle (kg)
$β^$	Dirac beta matrix

About this formula

FieldPhysics
TopicQuantum mechanics
LevelAdvanced
Also calledrelativistic wave equation for electrons, relativistic quantum wave equation, Dirac wave equation, relativistic Schrodinger equation, spin-1/2 relativistic equation, Dirac equation for free particle
SourceWikidata Q272621

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