  Gravitational field is usually neglected in calculation of atomic energy
levels as its effect is much weaker than the electromagnetic field, but that is
not the case for a particle orbiting a black hole. In this work, canonical
quantization of a particle under a gravitational field exerted by this tiny but
very massive object, both static and rotating-is carried out. By using this
method, very rare exact result of the particles quantized energy can be
discovered. The presence of a very strong attractive field and the horizon make
the energy complex valued and force the corresponding wave function to be a
quasi-bound state. Moreover, by taking a small scale limit, the system becomes
a gravitational atom in sense that hydrogenic atoms energy levels and wave
functions can be recovered. Obtaining these exact solutions for fundamental
black holes effectively empowers us to deal with more complex black holes such
as cosmological black holes or black hole solutions emerging from modified
gravity.
