  Semiclassical quantization is exact only for the so called \emph{solvable}
potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the
semiclassical phase, given by a series in $\hbar$, yields more or less
approximate results and eventually diverges due to the asymptotic nature of the
expansion. A quantum phase is derived to bypass these shortcomings. It achieves
exact quantization of nonsolvable potentials and allows to obtain the quantum
wavefunction while locally approaching the best pre-divergent semiclassical
expansion. An iterative procedure allowing to implement practical calculations
with a modest computational cost is also given. The theory is illustrated on
two examples for which the limitations of the semiclassical approach were
recently highlighted: cold atomic collisions and anharmonic oscillators in the
nonperturbative regime.
