光子的能量hv=E_{f}-E_{i} (1)
Bohr 曾应用电子能级的概念成功地解释了氢原子的光谱experiments.

跃迁的几率与电子的初始态和终态wave functions 有关.
严格数学表达应该是
W_{i->j} is proportional to <Psi_{i}|P|Psi_{j}>\delta(E-E_{i}-E_{j}) (2)
where P is momentum operator.

In summary, eq. (1) determines the light wavelength
and eq.(2) is corresponding to the light strength.

How about the vibration?
Due to the coupling between electronic states and vibration states, the electronic final state will be rearranged.
In solid, the lattice vibration (or phonon) plays a role to maintain momentum conservation for the transition process.

上述仅是物理概念的介绍。
具体的体系需要详细的研究。