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—an illustration of how the "planetary orbit" conception of electron motion differs from reality.