  In this work we explicitly show resurgence relations between perturbative and
one instanton sectors of the resonance energy levels for cubic and quartic
anharmonic potentials in one-dimensional quantum mechanics. Both systems
satisfy the Dunne-Unsal relation and hence we are able to derive one-instanton
non-perturbative contributions with the fluctuation terms to the energy merely
from the perturbative data. We confirm our results with previous results
obtained by Zinn-Justin et al.
