Oscillator strength quantum mechanical relations

The oscillator strength 7 is related to (from quantum mechanics) the probability of transition of an electron from one band to the next. 

It is interesting that there is a relation between the oscillator strength f (given by Eq. 2.6) and the square of the transition moment integral, which bridges the gap between the classical and quantum mechanical approaches ... 

The corresponding quantum mechanical expression of s op in Equation (4.19) is similar except for the quantity Nj, which is replaced by Nfj. However, the physical meaning of some terms are quite different coj represents the frequency corresponding to a transition between two electronic states of the atom separated by an energy Ticoj, and fj is a dimensionless quantity (called the oscillator strength and formally defined in the next chapter, in Section 5.3) related to the quantum probability for this transition, satisfying Jfj fj = l- At this point, it is important to mention that the multiple resonant frequencies coj could be related to multiple valence band to conduction band singularities (transitions), or to transitions due to optical centers. This model does not differentiate between these possible processes it only relates the multiple resonances to different resonance frequencies. 

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