Does a black hole have a wave function? Matter falling into a black hole has a wave function. Is the wave function of this matter destroyed or converted to information on the surface of the black hole? Does the information on the surface of the black hole have a wave function?
There is a series of papers by Gerard ’t Hooft available on arxiv where he discusses the quantum description of black holes, information paradox, etc. Few links below:
The quantum black hole as a theoretical lab, a pedagogical treatment of a new approach https://arxiv.org/abs/1902.10469
Discreteness of Black Hole Microstates https://arxiv.org/abs/1809.05367
What happens in a black hole when a particle meets its antipode https://arxiv.org/abs/1804.01383
The firewall transformation for black holes and some of its implications https://arxiv.org/abs/1612.08640
The Quantum Black Hole as a Hydrogen Atom: Microstates Without Strings Attached https://arxiv.org/abs/1605.05119
I think you may find some answers there.