Convergence properties and resummation of the 1/Dexpansion
Douglas J. Doren, Dudley R. Herschbach · Physical Review A · 1986
The semiclassical large-D expansion, with D the number of spatial dimensions, is very effective for some quantum-mechanical problems but not for those with singular potentials. We offer two ways to identify which systems will be poorly approximated by low orders of the 1/D series and show how to repair the difficulty in singular potential problems. The Yukawa potential and ${r}^{2}$+${\mathrm{gr}}^{4}$ anharmonic oscillator are presented as examples. We also discuss the large-order behavior of the 1/D series for the Yukawa problem and argue that this series is divergent.