  The Nekrasov-Shatashvili limit of beta-ensembles with polynomial potential
and N=2 supersymmetric gauge theories in the Omega-background is intimately
related to complex one-dimensional quantum mechanics. Multi-instanton
corrections in quantum mechanics, inferable from exact quantization conditions,
imply additional non-perturbative corrections to the Nekrasov-Shatashvili free
energies. Besides filling some of the gaps in previous derivations, we present
analytic expressions for such additional non-perturbative corrections in the
case of SU(2) gauge theory expanded at strong coupling. In contrast, at weak
coupling these additional non-perturbative corrections appear to be negligible.
