Many thanks for going through this. The dimensionality of Eq. (30) appears to be correct. The term in brackets is energy and when divided by m c squared is dimensionless. So the term becomes the usual gyromagnetic ratio (e h bar / (2m)) multiplied by sigma dot B multiplied by a dimensionless constant. This can be run through Maxima to double check. Very many new ESR, NMR, MRI and Zeeman and anomalous Z|eeman spectroscopies emerge – again by scholarly scrutiny of the ninety year old basics. I think that there will also be a whole pile of new results in nonlinear optics and quantum optics. Something for the younger generations to think about. In ECE two all this theory is related to torsion and curvature and spin connection.
Sent: 27/10/2015 19:45:50 GMT Standard Time
Subj: note 330(7)
How did you get the constants in eq.(30)? Eq. (28) is
< 1/r > = 1 / (n^2*a0)
with Bohr radius a0. Inserting this into (27) gives (30) but with m
instead of m squared. I do not know if (29) is correct.