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تسجيل مستخدم جديدOn connection between perturbation theory and semiclassical expansion in quantum mechanics
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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.
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