Abstract:
The classical approximation ($l=n-1\to\infty$) for the energy $\varepsilon^{(0)}$ and
the semiclassical expansion in problems of quantum mechanics are discussed. A recursive method is proposed for calculating the quantum corrections of arbitrary order
to $\varepsilon^{(0)}$, this being valid for both bound and quasistationary states. The generalization of the method to states with an arbitrary number of nodes and the
possibility of a more general choice of the parameter of the
semiclassical expansion are considered. The method is illustrated
by the example of the Yukawa and “funnel” potentials and for the
Stark effect in the hydrogen atom. These examples demonstrate
the rapid convergence of the $1/n$ expansion even for small quantum numbers.