  We apply the exact WKB analysis to a couple of one-dimensional
Schroedinger-type equations reduced from the Stark effect of hydrogen in a
uniform electric field. By introducing Langer's modification and incorporating
the Stokes graphs, we prove the exactness of the Bohr-Sommerfeld quantization
conditions for the Borel-resummed quantum WKB periods in the specific parameter
regions of the electric field intensity and magnetic quantum number. It is also
found these quantization conditions get modified with an additional suppressed
contribution when the parameters vary beyond the specific regions. We also
present Thermodynamic Bethe Ansatz (TBA) equations governing the quantum
periods in the absence of Langer's modification and discuss its wall-crossing
and analytic continuation. Numerical calculations are conducted to compare the
complex resonant frequencies from our quantization conditions against ones from
the Riccati-Pade method, the TBA equations are also confirmed by comparing its
expansions with all-order quantum periods.
