Larmor Frequency for Spin Transition

Question

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/larmor.html

Consider the process of Larmor precession of the magnetic moment associated with the spin angular momentum of an electron inside a hydrogen atom (ref. above link).

It is written that there is an "....angular frequency associated with the spin transition involving an energy change...".

But angular frequency is usually defined for rotating bodies. How can it be associated with the process of an energy transition, just as in this case? I can't imagine a rotating body in a spin-transition process!

Also, the energy difference and the angular frequency are related to each other using - 
$E = hbar omega$. Where did this come from?

ignacio · Answer

When you have two levels separated by energy $Delta E$, you can induce a transition between them by introducing a time-dependent term to the hamiltonian (for example exciting it with a periodic electromagnetic field). This term must have a time dependence of the form $cos(omega t)$ with $omega=frac{Delta E}{hbar}$. The angular frequency being referred to is $omega$, there are no rotating bodies here.

In order to understand why time-dependent perturbations of a certain frequency induce transitions between certain levels, you need to read up on time-dependent perturbation theory. Both Cohen and Sakurai are great sources for this.

Larmor Frequency for Spin Transition

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