  It is shown that for one-dimensional anharmonic oscillator with potential
$V(x)= a x^2+\ldots=\frac{1}{g^2}\,\hat{V}(gx)$ (and for perturbed Coulomb
problem $V(r)=\frac{\alpha}{r} + \ldots = g\,\tilde{V}(gr)$) the Perturbation
Theory in powers of coupling constant $g$ (weak coupling regime) and
semiclassical expansion in powers of $\hbar^{1/2}$ for energies coincide. %The
same is true for strong coupling regime expansion in inverse fractional powers
in $g$ of energy. It is related to the fact that the dynamics developed in two
spaces: $x\ (r)$-space and in $gx\ (gr)$ space, leads to the same energy
spectra. The equations which govern dynamics in these two spaces, the
Riccati-Bloch equation and the Generalized Bloch(GB) equation, respectively,
are presented. It is shown that perturbation theory for logarithmic derivative
of wave function in $gx\ (gr)$ space leads to true semiclassical expansion in
powers of $\hbar^{1/2}$ and corresponds to flucton calculus for density matrix
in path integral formalism in Euclidean (imaginary) time.
