Treatment of the hydrogen atom in an electric field by the path-integral formalism

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Abstract
The Feynman path-integral method is applied to solve the problem of a H atom in an electric field. In accordance with the midpoint philosophy, the propagators are symmetrized in every time interval and, via several transformations, one of which is the Langer modification, the Green’s function is calculated in parabolic coordinates, decomposed into partial propagators, and expressed in terms of two one-dimensional Green’s functions. The perturbation method being no more valid for high excited levels, the spectrum is given, according to the WKB method, as a solution of a system of two elliptic integral equations. The exact spectrum of the H atom is obtained for a zero electric field.

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