The Schrödinger equation is not relativistically invariant. In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. The Dirac Equation We will try to find a relativistic quantum mechanical description of the electron.
There was no explanation of the gyromagnetic ratio of 2. The Dirac equation can also be written in the concise form (2) (Griffiths 1987, p. 216), where (3) are Dirac matrices in the "Dirac basis" (Griffiths 1987, p. 216), and Einstein summation has been used to sum over , 1, 2, 3. Also we would like to have a consistent description of the spin of the electron that in the non-relativistic theory has to be added by hand. x (5.21) Substituting the fermion wavefunction, ψ, into the Dirac equation: (γµp µ −m)u(p) = 0 (5.22) 27. 1. The Dirac Equation Our goal is to find the analog of the Schrödinger equation for relativistic spin one-half particles, however, we should note that even in the Schrödinger equation, the interaction of the field with spin was rather ad hoc. The Dirac equation is one of the two factors, and is conventionally taken to be p m= 0 (31) Making the standard substitution, p !i@ we then have the usual covariant form of the Dirac equation (i @ m) = 0 (32) where @ = (@ @t;@ @x;@ @y;@ @z), m is the particle mass and the matrices are a set of 4-dimensional matrices. In its free form, or including electromagnetic interactions, it describes all spin-1 / 2 massive particles such as electrons and quarks for which parity is a symmetry.
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