An atom or a molecule can absorb light and undergo a transition from
one quantum state to another.
The oscillator strength  of a transition from a lower state
 to an upper state  may be defined by
where  is the mass of an electron and  is
the reduced Planck constant. The quantum states  1,2, are assumed to have several
degenerate sub-states, which are labeled by . "Degenerate" means
that they all have the same energy .
The operator  is the sum of the x-coordinates 
of all  electrons in the system, i.e.
The oscillator strength is the same for each sub-state .
The definition can be recast by inserting the Rydberg energy  and Bohr radius 
In case the matrix elements of  are the same, we can get rid of the sum and of the 1/3 factor