Unified derivation of the perturbation series for the real and imaginary parts of the energy of hydrogen in the stark effect and of the negatively anharmonic oscillator

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Abstract
The wave function for hydrogen in the Stark effect (or for the negatively anharmonic oscillator) with an outgoing‐wave boundary condition, constructed in Langer‐Cherry fJWKB form, is continued back to the origin. The asymptotic expansions for ReE and ImE are determined by the requirement that the wave function be regular at the origin to zeroth and first order in the exponentially small parameter that characterizes ImE. One fJWKB function turns out to be the Rayleigh‐Schrödinger perturbation theory wave function.
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