An analytic approach to the hydrogen Stark effect in weak, strong, and ultrastrong fields

Abstract

An accurate analytic approximate solution of the hydrogen-Stark-effect Schrödinger equation is obtained. In contrast to previous non-numerical solutions, this solution (which is piecewise continuous, and easily calculable) is accurate for applied electric fields of arbitrary strength—including weak fields ($F\lesssim 0.1F_{\mathrm{ion}}$; the Stark-shift regime), strong fields ($F\lesssim F_{\mathrm{ion}}$), and ultrastrong fields ($F\gtrsim {10}^2{F}_{\mathrm{ion}}$), where $F_{\mathrm{ion}}=3\mathrm{}\times {10}^8$ V / cm is the classical ionization field of hydrogen. The ultrastrong-field regime is experimentally accessible in solid-state physics where, for hydrogenic excitons, $F_{\mathrm{ion}}$ may be as small as ${10}^2$ V / cm.