Weyl sums and atomic energy oscillations
In the paper certain sums that play a crucial role in the asymptotic analysis of non-relativistic atomic energies are studied in great detail. To this purpose, the authors extend the usual Van der Corput's method for exponential sums (involving Poisson's summation plus stationary phase analysis) in order to study the oscillating term appearing in the quantum theory of large atoms. The authors manage to obtain an interpretation of the phenomena in terms of classical dynamics and produce in the paper sharp asymptotic upper and lower bounds for the oscillations.
asymptotic analysis of non-relativistic atomic energies
Van der Corput's method for exponential sums
sharp asymptotic upper and lower bounds for the oscillations
scientific article; zbMATH DE number 766474