[Train]

According to my textbook, UV absorption bands are not discrete lines because a single electronic transition can be accompanied by a number of vibrational and rotational transitions.  So one wavelength might cause a transition from E0, V0 to E1, V0 while a nearby wavelength might cause a transition from E0, V0 to E1, V1.

My question is, does this imply that a photon is somehow divisible, since in the second case part of the photon's energy is going to changing the energy of an electron and part is going to changing the vibrational energy of the molecule?  How does that work?

[Yggdrasil]

Although we can treat the rotational, vibrational, and electronic wavefunctions as separate entities, they are all part of the overall wavefunction of the molecule.  So, you can transfer all of the energy in the photon to go from a state like (E0,V0) --> (E1,V1).

As an analogy, consider striking a single windchime with a stick.  With one strike, you can get the windchime to ring, swing back and fourth, and even rotate.