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Bender-Wu Formula and the Stark Effect in Hydrogen

Benassi, L. and Grecchi, V. and Harrell, E. and Simon, B. (1979) Bender-Wu Formula and the Stark Effect in Hydrogen. Physical Review Letters, 42 (11). pp. 704-707. ISSN 0031-9007. doi:10.1103/PhysRevLett.42.704.

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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 arg E → −π/3, ∣E∣ ∼α[F(lnF)^(2/3) for F, the electric field strength, going to infinity). We also announce a rigorous proof of Bender-Wu-type formulas.

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Simon, B.0000-0003-2561-8539
Additional Information:© 1979 American Physical Society. (Received 23 October 1978) It is a pleasure to thank S. Graffi and I. Herbst for their interest and valuable comments. This research was supported in part by the National Science Foundation, Grant No. MCS 78-01885 and in part by the Istituto Nazionale di Fisica Nucleare, Sezione di Bologna. One of us (E.H. ) acknowledges receipt of a National Science Foundation National Needs Fellowship.
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NSFMCS 78-01885
Istituto Nazionale di Fisica Nucleare (INFN)UNSPECIFIED
Issue or Number:11
Record Number:CaltechAUTHORS:20180417-154002869
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85923
Deposited By: George Porter
Deposited On:18 Apr 2018 23:05
Last Modified:15 Nov 2021 20:33

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