Recently, it was realized that nonperturbative instanton effects can be generated to all orders by perturbation theory around a degenerate minima via the Dunne-Ünsal relation in several quantum mechanical systems. In this work we verify the Dunne-Ünsal relation for resonance energy levels of one-dimensional polynomial anharmonic oscillators. We show that the relation is applicable to cubic and quartic anharmonic oscillators which are genus-one potentials. However for higher order (higher genus) anharmonic potentials the relation is not satisfied and is subject to a certain extension.

• Received 14 January 2016

DOI:https://doi.org/10.1103/PhysRevD.93.065037