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We illustrate the physical significance and mathematical origin of resurgenttrans-series expansions for energy eigenvalues in quantum mechanical problemswith degenerate harmonic minima, by using the uniform WKB approach. We provideevidence that the perturbative expansion, combined with a global eigenvaluecondition, contains all information needed to generate all orders of thenon-perturbative multi-instanton expansion. This provides a dramaticrealization of the concept of resurgence, whose structure is naturally encodedin the resurgence triangle. We explain the relation between the uniform WKBapproach, multi-instantons, and resurgence theory. The essential idea appliesto any perturbative expansion, and so is also relevant for quantum fieldtheories with degenerate minima which can be continuously connected to quantummechanical systems.

Uniform WKB, Multi-instantons, and Resurgent Trans-Series