Relativistic quantum mechanics

Relativistic quantum mechanics combines quantum principles with special relativity to describe particles at high speeds, using equations such as the Dirac and Klein–Gordon equations.

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Dirac equation: A relativistic wave equation for spin-one-half particles that predicts antimatter. It incorporates electron spin and yields the positron as a positive-energy solution.
Quantum mechanics: The theory describing matter and radiation through states, probabilities, and quantized observables. Relativistic quantum mechanics extends its state-based framework to relativistic regimes.
Schrödinger equation: The nonrelativistic wave equation governing the time evolution of a quantum state. It works at low speeds but does not satisfy special-relativistic symmetry.
Electron: A negatively charged elementary particle with spin one-half. The Dirac equation was developed to describe the electron consistently with special relativity.
Paul Dirac: A British theoretical physicist who formulated the relativistic electron equation and helped establish quantum mechanics. His 1928 equation joined quantum theory with special relativity and implied antimatter.
Relativistic energy–momentum relation: The special-relativistic relation connecting energy, momentum, and rest mass. Relativistic quantum equations encode this relation in their particle-energy spectra.
Special relativity: The theory that space and time are linked and that physical laws are invariant in inertial frames. Its invariant speed and Lorentz symmetry constrain the form of relativistic quantum equations.
Pauli equation: A nonrelativistic wave equation for spin-one-half particles in electromagnetic fields. It captures electron spin without providing a fully relativistic description.
Positron: The electron's positively charged antiparticle. Its existence emerged from interpreting the Dirac equation's solutions.
Erwin Schrödinger: An Austrian physicist who formulated the wave equation central to nonrelativistic quantum mechanics. His earlier relativistic wave equation led to the Klein–Gordon equation, while his standard equation is nonrelativistic.