Stark effect in a hydrogenic atom or ion: treated by the phaseintegral method
by Nanny Froman , Per Olof Froman

Persian Title: اثر اشتارک در یک اتم یا یون hydrogenic : درمان با استفاده از روش فاز انتگرال

Summary and Info
This book treats the Stark effect of a hydrogenic atom or ion in a homogeneous electric field. It begins with a thorough review of previous work in this field since 1926. After the Schrodinger equation has been separated with respect to time dependence, centre of mass motion and internal motion, followed by a discussion of its eigenfunctions, the exact development in time of the probability amplitude for a decaying state is obtained by means of a formula analogous to the Fock Krylov theorem. From this formula one obtains by means of the phaseintegral approximation generated from a particular base function nonrelativistic formulas for profiles, energies and halfwidths of the Stark levels. These formulas are then transformed into formulas expressed in terms of complete elliptic integrals. The formulas thus obtained are used for the calculation of energies and halfwidths of 198 different Stark states, which are compared with the corresponding results obtained by other authors with the use of other methods. An analysis of this material indicates that the energy values obtained by the phaseintegral method are at least as accurate as those obtained by other methods in more than half of the 198 cases. The book presents one of the most comprehensive asymptotic treatments of the Stark effect in atomic hydrogen that have been published. Contents: Schrodinger Equation, its Separation and its Exact Eigenfunctions; Development in Time of the Probability Amplitude for a Decaying State; PhaseIntegral Method; Derivation of PhaseIntegral Formulas for Profiles, Energies and HalfWidths of Stark Levels; Procedure for Transformation of the PhaseIntegral Formulas into Formulas Involving Complete Elliptic Integrals; PhaseIntegral Quantities and Their Partial Derivatives with Respect to E and Z1 Expressed in Terms of Complete Elliptic Integrals.
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