OK thanks, that gives the right units. I've found conflicting expressions: these two pages both have a factor of ##c## and so do the lecture notes I'm working from:
http://ocw.usu.edu/physics/classical-mechanics/pdf_lectures/13.pdf
https://en.wikipedia.org/wiki/Larmor_precession
but this one...
Take a spin-1/2 particle of mass ##m## and charge ##e## and place it in a magnetic field in the ##z## direction so that ##\mathbf B=B\mathbf e_z##. The corresponding Hamiltonian is
$$\hat H=\frac{eB}{mc}\hat S_z.$$
This must have units of joules overall, and since the eigenvalues of ##\hat S_z##...
Let's say ##f(x)=ax^2##. Then ##d^2f/dx^2=2a##.
Now we can make the change of variables ##y\equiv\sqrt ax## to give ##f(y)=y^2##. Then ##d^2f/dy^2=2##.
It follows that
##\frac{d^2f}{dx^2}=a\frac{d^2f}{dy^2},##
but I can't replicate this with the chain rule.
I would put...