Stark Effect in Hydrogen*

This paper gives a theoretical treatment of atomic hydrogen in an external electric field. The positions and half-widths of the energy levels which are near the peak of the effective potential barrier are found. The problem is solved by applying Wentzel–Kramers-Brillouin–type approximations to the Schrödinger equation separated in parabolic coordinates; the usual perturbation treatment does not apply to these high levels. Formulas for the levels and half-widths are found in terms of complete elliptic integrals.