  We study in detail the Schr\"{o}dinger equation corresponding to the four
dimensional $SU(2)$ $\mathcal{N}=2$ SQCD theory with one flavour. We calculate
the Voros symbols, or quantum periods, in four different ways: Borel summation
of the WKB series, direct computation of Wronskians of exponentially decaying
solutions, the TBA equations of Gaiotto-Moore-Neitzke/Gaiotto, and instanton
counting. We make computations by all of these methods, finding good agreement.
We also study the exact quantization condition for the spectrum, and we compute
the Fredholm determinant of the inverse of the Schr\"odinger operator using the
TS/ST correspondence and Zamolodchikov's TBA, again finding good agreement. In
addition, we explore two aspects of the relationship between singularities of
the Borel transformed WKB series and BPS states: BPS states of the 4d theory
are related to singularities in the Borel transformed WKB series for the
quantum periods, and BPS states of a coupled 2d+4d system are related to
singularities in the Borel transformed WKB series for local solutions of the
Schr\"odinger equation.
