I have been asked to consider an atom formed between an electron and 'black hole' i.e. a point singularity with mass and no charge. I should find the mass of the black hole Mh such that the energy levels of this atom would be identical to the energy levels of a hydrogen atom
I'm fairly sure I can calculate a mass that would give the same energy of the n=1 orbital (13.6eV) at the Bohr radius a0 by considering gravitational rather than EM interactions, but I'm having difficulty grasping the notion of quantised gravitational orbits. Are all 'energy levels' quantised?