Before the creation of quantum field theory, physicists attempted to formulate versions of the Schrödinger equation which were compatible with special relativity. Such equations are called relativistic wave equations.

The first such equation was discovered by Erwin Schrödinger himself; however, he realized that this equation, now called the Klein-Gordon equation, gave incorrect results when used to calculate the energy levels of hydrogen. Schrödinger discarded his relativistic wave equation, only to realize a few months later that its nonrelativistic limit (what is now called the Schrödinger equation) was still of importance.

List of relativistic wave equations

1. Klein-Gordon equation:describes a massless or massive spin-0 particle
2. Weyl equation : describes a massless spin-1/2 particle
3. Dirac equation: describes a massive Dirac particle
4. Majorana equation : describes a massive Majorana particle
5. Breit equation : describes two massive spin-1/2 particles interacting electromagnetically to first order in perturbation theory
6. Maxwell equations: describe a massless spin-1 particle
7. Proca equation: describes a massive spin-1 particle
8. Kemmer equation : an alternative equation for spin-1 particles
9. Rarita-Schwinger equation: describes a massive spin-3/2 particle
10. Bargmann-Wigner equations : describe free particles of arbitrary integral or half-integral spin
11. quantum field theory: describes relativistic quantum fields
12. Yang-Mills equation: describes a non-abelian gauge field
13. Yang-Mills-Higgs equation : describes a non-abelian gauge field coupled with a massive spin-0 particle

All the particle equations except the Breit equation are linear. The Yang-Mills and Yang-Mills-Higgs equations are non-linear.

See also

• Status of special relativity