  We propose a new exact quantization condition for a class of quantum
mechanical systems derived from local toric Calabi-Yau three-folds. Our
proposal includes all contributions to the energy spectrum which are
non-perturbative in the Planck constant, and is much simpler than the available
quantization condition in the literature. We check that our proposal is
consistent with previous works and implies non-trivial relations among the
topological Gopakumar-Vafa invariants of the toric Calabi-Yau geometries.
Together with the recent developments, our proposal opens a new avenue in the
long investigations at the interface of geometry, topology and quantum
mechanics.
