I was recently revisiting Norton's dome and was reading about its connect with Bohmian mechanics. I completely understand its role in classical physics, but a more fundamental question would be: Is a quantum version of the Norton dome possible, where the wave function is bound to the surface. What would be the energy Eigen state which would have exactly the same amount of energy necessary for a classical particle to rest on the dome, assuming the angular momentum of this state to be zero? How would this change with a non-zero angular momentum?

Does the dome point out any anomalies in quantum mechanics as it did in classical physics?