Restricted quantum-mechanical three-body problems. I - One moving electron in the field of two coulombic ions which are fixed in space

Astronomy and Astrophysics – Astrophysics

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Electron Scattering, H Lines, Hydrogen Ions, Quantum Mechanics, Schroedinger Equation, Three Body Problem, Asymptotic Methods, Eigenvalues, Power Series, Spectral Line Width, Wave Functions

Scientific paper

The Schroedinger equation is solved if an electron moves in the field of charges Z1 and Z2 which are fixed in space. The wave function is expanded in power series, the eigenvalues are given graphically and partly in tabular form. The asymptotic behavior of the eigenvalues is discussed when the distance of the two fixed charges is small and large. Some consequences are drawn on hydrogen line broadening, shift and grenzkontinua. Further utilization of the calculations is indicated. The mathematical appendix helps to clarify some technical details of the calculations.

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