  We prove that the topological recursion formalism can be used to quantize any
generic classical spectral curve with smooth ramification points and simply
ramified away from poles. For this purpose, we build both the associated
quantum curve, i.e.~the differential operator quantizing the algebraic equation
defining the classical spectral curve considered, and a basis of wave
functions, that is to say a basis of solutions of the corresponding
differential equation. We further build a Lax pair representing the resulting
quantum curve and thus present it as a point in an associated space of
meromorphic connections on the Riemann sphere, a first step towards
isomonodromic deformations. We finally propose two examples: the derivation of
a 2-parameter family of formal trans-series solutions to Painlev\'e 2 equation
and the quantization of a degree three spectral curve with pole only at
infinity.
