 A more accurate description of the hydrogen atom comes from a purely quantum mechanical treatment that uses the Schrödinger equation , Dirac equation or even the Feynman path integral formulation to calculate the probability density of the electron around the proton . The most complicated treatments allow for the small effects of special relativity and vacuum polarization . In the quantum mechanical treatment , the electron in a ground state hydrogen atom has no angular momentum at all — illustrating how the " planetary orbit " differs from electron motion . 
