In 1928, building on Pauli's work on nonrelativistic spin systems, he derived the [Dirac equation]?, a relativistic equation describing the electron. This allowed Dirac to predict the existence of the positron, the electron's anti-particle; the positron was subsequently observed by Anderson in 1932.
His Principles of Quantum Mechanics, published in 1930, pioneered the use of linear operators as a generalization of the theories of Heisenberg and Schrödinger. It also introduced the bra-ket notation, in which |ψ> denotes a state vector in the Hilbert space of a system and <ψ| its dual vector.
He shared the Nobel Prize for physics in 1933 with Erwin Schrodinger "for the discovery of new productive forms of atomic theory".
Dirac was Lucasian professor of mathematics at Cambridge from 1932 to 1969. The [Dirac Prize]? is awarded in his honour.
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