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Dirac Equation


\LARGE(i{\hbar}c\gamma^\mu\partial_\mu-mc^2)\psi=0



The Terms

i - Imaginary unit i=\sqrt{-1}

\hbar - Planck's constant divided by 2\pi  [Value: 1.051 × 10-34 m2 kg s-1]

 c - The speed of light [Value: 3 × 108 m s-1]

\gamma^\mu - Dirac matrices

\partial_\mu - Four-gradient, \partial_\mu=\left(\frac{1}{c}\frac{\partial}{{\partial}t},\boldsymbol{\nabla}\right)

m - Rest mass of the electron [Value: 0.511 MeV / c2]

\psi - Wavefunction of the system - the probability amplitude for different configurations of the system at different times. Also known as the quantum state, this is the most complete description that can be given to a physical system.




What Does It Mean?

The Dirac Equation is a relativistic quantum mechanical wave equation which provides a description of spin-1/2 particles, such as electrons, consistent with quantum mechanics and special relativity. This equation predicts the existence of antiparticles and predates their actual experimental discovery.



Further information at Warwick

The Dirac Equation is covered in our fourth year modules "PX408 Relativistic Quantum Mechanics" and "PX430 Gauge Theories for Particle Physics".

dirac

Paul Dirac

1902-1984