  The problem of finding the large order asymptotics for the eigenfunction
perturbation theory in quantum mechanics is studied. The relation between the
wave function argument x and the number of perturbation theory order k that
allows us to construct the asymptotics by saddle-point technique is found:
$x/k^{1/2}=const$, k is large. Classical euclidean solutions starting from the
classical vacuum play an important role in constructing such asymptotics. The
correspondence between the trajectory end and the parameter $x/k^{1/2}$ is
found. The obtained results can be applied to the calculation of the main
values of the observables depending on k in the k-th order of perturbation
theory at larges k and, probably, to the multiparticle production problem.
