The gyromagnetic ratio or g factor of the electron is correctly predicted by the Dirac equation to be 2. However, it is also possible to obtain this value from nonrelativistic quantum mechanics, as shown by Sakurai, who credits Feynman. It is noted here that the same trick used by Sakurai allows a factorization of the time independent Pauli equation. The result is an equivalent first‐order equation which is referred to as the spin‐momentum equation. In the absence of a scalar potential, the spin‐momentum equation is the eigenvalue equation for the inner product of spin and kinetic momentum operators. The spin‐momentum equation is solved directly for a constant magnetic field, and the solution is compared with the well‐known Pauli equation solutions.
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September 01 1992
The electron g factor and factorization of the Pauli equation
Ronald J. Alder;
Ronald J. Alder, Robert A. Martin; The electron g factor and factorization of the Pauli equation. Am. J. Phys. 1 September 1992; 60 (9): 837–839. https://doi.org/10.1119/1.17066
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