Solving Shrodinger Equation for Hawking Radiation

[Wishbone]

I hear this is a result of quantum tunneling, what I am wondering is, can one solve the shrodinger equation for black holes under the idea that it is just a really really really deep finite well?

 

[Igor_S]

Isn't Hawking radation a process in which a virtual particle (like virtual photon) traveling near the horizon creates particle-antiparticle pair, but before they get to annihilate, black hole pulls in one of them, and other one escapes ? (that creates some sort of a radiation)