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In this paper a description of the small-$\hbar$ limit of loci of zeros offundamental solutions for polynomial potentials is given. The considered casesof the potentials are bounded to the ones which provided us with simple turningpoints only. Among the latter potentials still several cases of Stokes graphsthe potentials provide us with are distinguished, i.e. the general non-criticalStokes graphs, the general critical ones but with only single internal Stokesline and the Stokes graphs corresponding to arbitrary multiple-well real evendegree polynomial potentials with internal Stokes lines distributed on the realaxis only. All these cases are considered in their both versions of thequantized and not quantized $\hbar$. In particular due to the fact that thesmall-$\hbar$ limit is semiclassical it is shown that loci of roots offundamental solutions in the cases considered are collected along Stokes lines.There are infinitely many roots of fundamental solutions on such lines escapingto infinity and a finite number of them on internal Stokes lines.

The semiclassical small-$\hbar$ limit of loci of roots of fundamental solutions for polynomial potentials