  We study the Argyres-Douglas theories realized at the superconformal point in
the Coulomb moduli space of $\mathcal{N}=2$ supersymmetric $SU(2)$ QCD with
$N_f=1,2,3$ hypermultiplets in the Nekrasov-Shatashvili limit of the
Omega-background. The Seiberg-Witten curve of the theory is quantized in this
limit and the periods receive the quantum corrections. By applying the WKB
method for the quantum Seiberg-Witten curve, we calculate the quantum
corrections to the Seiberg-Witten periods around the superconformal point up to
the fourth order in the parameter of the Omega background.
