The Spin of the Electron

Abstract

In this chapter we explain the origin of the intrinsic angular momentum, also known as the spin, of the electron on the basis of the Dirac equation. After introducing the Dirac equation for a relativistic massive and charged particle coupled to the electromagnetic field, we study its non relativistic limit deriving the Pauli equation. This Pauli equation, which is nothing else than the Schrödinger equation with an additional term containing the spin operator, predicts very accurately the magnetic moment of the electron. Finally, we discuss the relativistic hydrogen atom and the fine-structure corrections to the non relativistic one.

Further Reading

For the Dirac equation and the Pauli equation:

J.D. Bjorken and S.D. Drell, Relativistic Quantum Mechanics, chapt. 1, sections 1.1, 1.2, 1.3, 1.4 (McGraw-Hill, New York, 1964).

For the relativistic hydrogen atom and the fine splitting:

V.B. Berestetskii, E.M. Lifshitz, L.P. Pitaevskii, Relativistic Quantum Theory, vol. 4 of Course of Theoretical Physics, chapt. 4, sections 34, 35, 36 (Pergamon Press, Oxford, 1971).

B.H. Bransden and C.J. Joachain: Physics of Atoms and Molecules, chapt. 5, sections 5.1 (Prentice Hall, Upper Saddle River, 2003).