The hydrogen atom is an example of a central-force system
(a two-particle system in which the potential energy depends only on the
distance between the two particles).
The Schrödinger equation for the hydrogen atom can be separated into
one equation for the motion of the center of mass and one equation for the
motion of the electron relative to the nucleus.
The relative Schrödinger equation can be solved in spherical polar
coordinates by separation of variables, assuming that
ψR(r)Θ(θ)Φ(φ). These wave functions are called orbitals.
The energy eigenvalues for the relative motion are the same as in the
Bohr theory.
The square of the orbital angular momentum of the electron and one
component of this angular momentum can have predictable values if a
hydrogen atom is in a state corresponding to an energy eigenfunction.
The angular momentum values are different from the Bohr theory.
Electrons have intrinsic (spin) angular momentum in addition to the
angular momentum of orbital motion.
