BENDER-WU FORMULA AND THE STARK EFFECT IN HYDROGEN

We discuss a close connection between the formula of Banks, Bender, and Wu for the asymptotics of the Rayleigh-Schrödinger coefficients of the two-dimensional rotationally symmetric anharmonic oscillator and the behavior of resonances of the hydrogen Stark problem in two regimes: small field (Oppenheimer's formula) and large field (where we obtain the new results argE→-π3, |E|∼α[F(lnF)]23 for F, the electric field strength, going to infinity). We also announce a rigorous proof of Bender-Wu-type formulas. © 1979 The American Physical Society.