Type: Article
Publication Date: 1979-03-12
Citations: 76
DOI: https://doi.org/10.1103/physrevlett.42.704
We discuss a close connection between the formula of Banks, Bender, and Wu for the asymptotics of the Rayleigh-Schr\"odinger 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 $\mathrm{arg}E\ensuremath{\rightarrow}\ensuremath{-}\frac{\ensuremath{\pi}}{3}$, $|E|\ensuremath{\sim}\ensuremath{\alpha}{[F(\mathrm{ln}F)]}^{\frac{2}{3}}$ for $F$, the electric field strength, going to infinity). We also announce a rigorous proof of Bender-Wu-type formulas.