  Starting from loop equations, we prove that the wave functions constructed
from topological recursion on families of degree $2$ spectral curves with a
global involution satisfy a system of partial differential equations, whose
equations can be seen as quantizations of the original spectral curves. The
families of spectral curves can be parametrized with the so-called times,
defined as periods on second type cycles, and with the poles. These equations
can be used to prove that the WKB solution of many isomonodromic systems
coincides with the topological recursion wave function, which proves that the
topological recursion wave function is annihilated by a quantum curve. This
recovers many known quantum curves for genus zero spectral curves and
generalizes this construction to hyperelliptic curves.
