  In this work we find that not only the Heisenberg-like uncertainty products
and the R\'enyi-entropy-based uncertainty sum have the same first-order values
for all the quantum states of the $D$-dimensional hydrogenic and
oscillator-like systems, respectively, in the pseudoclassical ($D \to \infty$)
limit but a similar phenomenon also happens for both the
Fisher-information-based uncertainty product and the Shannon-entropy-based
uncertainty sum, as well as for the Cr\'amer-Rao and Fisher-Shannon
complexities. Moreover, we show that the LMC (L\'opez-Ruiz-Mancini-Calvet) and
LMC-R\'enyi complexity measures capture the hydrogenic-harmonic difference in
the high dimensional limit already at first order.
