Abstract
A simple method for studying real singularities from power series expansions is developed. Singularity positions, critical exponents, and critical amplitudes are calculated for a number of quantum-mechanical eigenvalue problems. Special attention is devoted to the Z−1 perturbation series for two-electron atoms. Present results for the states (1s2) 1S, (2p2) 3P, and (1s2s) 3S reveal inaccuracies in previous calculations. In particular it is suggested that the singularity for the 3S state occurs at Z=1 and that the energy lies in the limit of the continuous spectrum of H−.
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