This note gives a simple and clear derivation of electron spin orbit coupling from the well known hamiltonian of the anomalous Zeeman effect. The origin of ESOR is the operator equation (7), which appears to have been missed completely in the subject of spin resonance. The spin S in quantum mechanics is a vector operator defined by
S = (1/2) h bar sigma
where sigma is the Pauli matrix. For real L and B
sigma dot L sigma dot B = L . B
but
sigma dot L sigma dot B psi is not equal to L. B psi
The ESOR resonance frequency is given in Eq. (12) and it shifts the ESR frequency and splits it due to a new type of spin orbit coupling which gives a new type of spectroscopy. This is another in quite a long list of new spectroscopies that I have discovered in the past forty years plus of research. In my experience it takes a long time for the experimentalists to catch up with the theory. However all of these new spectroscopies are archived in the UFT papers and Omnia Opera on www.aias.us and in the National Archives in the British Library in London on www.webarchive.org.uk, Sceince and Technology, AIAS.