Dirac Equation

The Dirac equation is a fundamental wave equation that satisfies the requirements of the special theory of relativity. Shortly after the appearance of the ► Schrodinger equation, several physicists attempted to extend it to the relativistic domain. The result — known as the Klein-Gordon-equation ► relativistic quantum mechanics — was however unable to describe ► electrons correctly. Paul A.M. Dirac realized that the formal structure of the Schrodinger equation, the form Hψ = i ℏ∂ψ/∂t, had to be retained also in a relativistic theory, implying that the ► Hamilton operator must be of the first order in the space derivatives. By “playing around with mathematics” he derived in late 1927 a wave equation which was linear in both space and time derivatives. For a free electron he wrote it as (W/c + α,i.p,/i. + βm ₀ c)ψ = 0, where the quantities α and β were 4×4 matrices. In later literature the matrices were often designated _γμ(μ = 1, 2, 3,4).