In the quantum harmonic oscillator, there exists a family of states called coherent states which form an overcomplete set of states. They are regarded as "the states most resembling classical states", in that their parameter satisfies the classical equation of motion of the harmonic oscillator. Multiple generalisations exist to diverse situations and have proven useful.
In TQFTs, we have Hilbert spaces and evolution operators as well, so do we also have coherent states of some sort? What are they being used for?
Bonus: Are there categorified versions of these in extended TQFTS?